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SLIDE VALVE GEARS 



AN EXPLANATION OF THE ACTION AND 

CONSTRUCTION OF PLAIN AND 

CUT-OFF SLIDE VALVES. 



BY / 

FREDERIC A. 'hALSEY, 

ENGINEER OF THE RAND DRILL COMPANY; 

Member of the American Society of Mechanical Engineers ; Member of 

the American Institute of Mining Engineers ; Graduate 

of the sibley college, cornell university. 




glnalssis b$ tfje Btlsram Btagram 




NEW YORK : 
D. VAN NOSTRAND COMPANY, 

23 Murray and 27 Warren Streets. 
1890. 



>Hvb 



Copyright, 1889, 

BY 

D. Van Nostrand Company. 



-**&* 



1/ 



TO 

Iprofessor $obn B. Sweet, 

TO HAVE BEEN WHOSE PUPIL I CONSIDER ONE OF THE 

GREATEST PRIVILEGES OF MY LIFE, 

THIS LITTLE VOLUME IS GRATEFULLY INSCRIBED. 



PREFACE. 



THIS work has been prepared to meet what the author 
considers a real want. It has been written with the aim 
of making it intelligible to any one who might be will- 
ing to make a serious effort to understand it. High 
authority exists for a mathematical treatment of the 
subject, but with this the author has no sympathy. 
Designing a valve gear is essentially a drawing board 
process, and a mathematical treatment of it is simply 
an uncalled for use of heavy artillery. The graphical 
treatment is therefore adopted throughout. 

Acknowledgment is due to Mr. Hugo Bilgram for 
his courtesy in kindly permitting the use of his valve 
diagram. The author has all due respect for the Zeu- 
ner diagram, but that respect is not incompatible with 
the conviction that Mr. Bilgram's method is a marked 
improvement upon it. Valve diagrams are used for two 
purposes — to analyze existing valve motions and to de- 
sign new ones. The Zeuner diagram fulfils the first pur- 
pose perfectly, but is unsatisfactory when applied to 
the second. The leading data that are given in design- 
ing a valve motion are the point of cut-off, the port open- 
ing, and the lead of the valve (not the lead angle of the 
crank, as is often conveniently assumed). It is the radi- 



IV PREFACE. 

cal defect of the Zeuner diagram that none of these di- 
mensions can be laid off from known points. The lead 
must be laid off from an unknown point of the centre 
line, and the port opening from an unknown point on 
an unknown line. Finally, through these unknown 
points and the centre of the shaft the valve circle is to 
be drawn from an unknown centre and with an unknown 
radius. Under these circumstances the result sought 
is found only through blind trial. With Mr. Bilgram's 
method all this is changed. The lead is laid off from a 
fixed line, the port opening from a fixed point, and the 
cut-off position of the crank is located. The lap circle 
is then drawn tangent to these lines, and the problem 
is solved. Moreover, the awkward conception of the 
backward rotation of the crank is obviated. Finally, 
these marked advantages are not accompanied by any 
compensating disadvantages whatever. 

Acknowledgment is also due to the American Ma- 
chinist for the use of a number of engravings originally 
prepared to illustrate some of the author's articles in 
that paper. 

The irregularities due to the connecting rod introduce 
peculiar difficulties into the study of the first principles 
of the slide valve, which difficulties were first overcome 
by the happy expedient of using the slotted cross-head 
instead of the connecting rod in the preliminary study. 
For this, together with many other original and highly 
valuable contributions to the subject, we are indebted 
to Mr. W. S. Auchincloss, who first published them in 
his well-known and standard work entitled Link and 
Valve Motions, to which those who wish to prosecute 
their studies beyond the scope of this work are referred. 



PREFACE. V 

The author has gone more fully than is customary 
into the methods of equalizing the various events of 
the stroke. The sections relating to these methods 
will be found more difficult to follow than the others, 
while at the same time they form no necessary part of 
a general treatment of the subject. Those who be- 
gin their studies of valve motions with this book, may 
find these chapters too difficult for the first reading. 
They have, therefore, been marked with a star (*)in the 
Table of Contents and in the body of the book, in order 
that they may be omitted, if desired, in the first reading; 
and it should be understood that the chapters not so 
marked form of themselves a complete connected trea- 
tise, of a more elementary character than the book as a 
whole. 

Philadelphia, Oct. 19, 1889. 



TABLE OF CONTENTS. 



The chapters with an asterisk (*) prefixed may be omitted in the first reading 
without breaking the continuity of the subject. 

PART I. 
The Slide Valve with Fixed Eccentric. 

PAGE 

The Plain Slide Valve, 3 

The Eccentric, .......... 4 

The Scotch Yoke or Slotted Cross-head, ..... 5 

The Primitive Engine, 7 

Defects of the Primitive Engine, . . . . . , 13 

Lap, 15 

Angular Advance, ......... 18 

Lead, 21 

Exhaust Lap, 25 

Backward Rotation, ......... 26 

The Bilgram Diagram, ....... . 28 

Laying out the Slide Valve, ....... 38 

* Velocity of the Valve, ... .... 39 

Limitations of the Plain Slide Valve, ...... 40 

The Areas of the Ports and Pipes, . . . . . 42 

* The Angular Vibration of the Connecting Rod, ... 45 

" Eccentric Rod, .... 49 

* Equalized Exhaust, ........ 50 

* Equalized Cut-off, 54 

Setting the Slide Valve. ........ 59 

vii 



Vlll TABLE OF CONTENTS. 



PART II. 



The Slide Valve with Shifting and Swinging Eccentric. 

PAGE 

The Slide Valve at Short Cut-off, . . . . . . 67 

* Equal Lead and Constant Lead, . . . . . . 77 

The Shifting Eccentric, 78 

The Swinging Eccentric, ........ 80 

* The Angularity of the Eccentric Rod, . . . . . 85 

* Equalized Lead, 89 

* Equalized Lead and Cut-off, . . . . . . . 95 



PART III. 

The Slide Valve with Independent Cut-off. 

Introductory Remarks, ........ 101 

The Gonzenbach Valve Gear, ....... 102 

The Meyer Valve Gear, . . . . . . . 109 

The Buckeye Valve Gear, . . . . . . . .116 

The Straight Line Independent Cut-off Valve Gear, . . .120 
The Bilgram Valve Gear, . . , . , . , .122 



Part I. 

THE SLIDE VALVE WITH FIXED 
ECCENTRIC. 



The Slide Valve with Fixed Eccentric. 



THE PLAIN SLIDE VALVE. 



Fig. I is a sectional view of a plain slide valve and 
its seat, the valve being shown in its central position, 
with the ports completely covered by it. The distance 




Fig.1 

a, by which the valve extends beyond the steam edge 
of the port, is called the outside lap, steam lap, or more 
usually, simply lap of the valve. The distance &, by 
which it extends beyond the exhaust edge of the port, 
is called the inside lap or exhaust lap.* The exhaust 

* As will be more fully shown later on, valves are sometimes so made 
that the steam is admitted by the inside and exhausted by the outside 
edges. Hence the terms inside and outside lap are somewhat am- 
biguous. The terms steam lap and exhaust lap avoid this ambiguity, 
and are to be preferred, 
3 



4 SLIDE VALVE GEARS. 

lap is always much smaller than the steam lap. It is 
frequently absent, and frequently the exhaust edge of 
the valve does not reach the exhaust edge of the port, 
being made as shown by the dotted lines. In that 
case the distance c is usually called inside clearance, 
though a better name is negative inside or exhaust lap. 
It is sometimes called inside lead or exhaust lead ; but 
these terms should not be applied here, as they have 
properly another definite meaning, which will be ex- 
plained farther on. The measurement for both steam 
and exhaust lap is made for one end of the valve only. 
Thus if a valve is said to have f inch lap, the meaning 
is that it has that much at each end. 



THE ECCENTRIC. 

The slide valve is usually driven by means of an eccen- 
tric on the crank shaft, and it becomes necessary at the 
outset to obtain a clear conception of the motion which 
the eccentric gives. In brief, the eccentric is a short 
crank with a large crank pin. It is obvious that the 
motion of a cross-head would not be changed by in- 
creasing the size of the crank pin. If a crank pin were 
enlarged until the crank shaft came within the cir- 
cumference of the pin, the result would be an eccen- 
tric. The arm of a crank is the distance from the 
centre of the shaft to the centre of the crank pin, and 
similarly the " throw'' of an eccentric is the distance 
from the centre of the shaft to the centre of the eccen- 
tric disc. Usually the centre of the disc is within 
the circumference of the shaft ; but this does not alter 



THE SCOTCH YOKE OR SLOTTED CROSS-HEAD. 5 

the nature of the device, which remains simply a short 
crank with a large crank pin. 



THE SCOTCH YOKE OR SLOTTED CROSS-HEAD. 

The usual method of connecting the cross-head to 
the crank pin by means of a connecting rod introduces 
certain distortions and irregularities into the relative 
motions of the piston and crank. These will be more 
fully explained farther on, but it is desirable in the 
first instance to avoid the necessity for considering 
them, as they greatly complicate the subject. This is 
accomplished by considering in the first instance an 
engine having the piston and crank connected by 
means of the device called the Scotch yoke or slotted 
cross-head, since that connection is without the distor- 
tions mentioned.* As has been explained, the eccen- 
tric is essentially a crank ; and it follows that the dis- 
tortions which are introduced by the connecting rod 
into the motions of the piston and crank, are also in- 
troduced by the eccentric rod into the motions of the 
valve and eccentric. The reasons which lead to the 
adoption of the slotted cross-head in place of the con- 
necting rod also require its use in place of the eccen- 
tric rod. An engine fitted with slotted cross-heads is 
illustrated in Figs. 2-1 1. The slotted cross-head will 
be recognized at once, and is too familiar a device to 
need further description. 



*The slotted cross-head is employed here with the permission of 
Mr. W. S. Auchincloss, to whom the thanks of the author are due. 



SLIDE VALVE GEARS. 




THE PRIMITIVE ENGINE. J 

THE PRIMITIVE ENGINE. 

When illustrating the action of the valve of a steam 
engine, it is essential for clearness that the valve be 
shown on the top of the cylinder. A valve so located 
in an actual engine would require the use of a rock 
shaft to communicate the motion of the eccentric rod 
to the valve rod — a construction which finds use in 
American locomotives. This rock shaft complicates 
the action of the parts, and it is desirable in this pre- 
liminary work to avoid it. To accomplish this the 
unmechanical arrangement of Figs. 2-1 1 is adopted. 

Figs. 2-6 represent the primitive engine with the 
parts in a number of successive positions. The valve 
has no lap on either steam or exhaust side, and the 
eccentric is set at right angles to the crank, and in ad- 
vance of it in the direction of the rotation. The ec- 
centric, being in fact a crank, is represented as such, 
and the valve is driven from it by a slotted cross-head, 
which is secured to the valve stem by the bracket 
shown. In Figs. 3-6 the slotted cross-heads are rep- 
resented by their centre lines only, for greater clearness 
and simplicity. 

Referring to Fig. 2, the crank is on the "centre," 
and the parts are ready to begin movement, the direc- 
tion of rotation being as shown by the arrow. In Fig. 
3 the crank shaft has turned through an angle of forty 
five degrees, carrying the parts to the positions shown. 
Considering Figs. 2 and 3, it is clear that the first move- 
ment of the crank shaft carried the valve to the right, 
and thereby opened port x to steam and y to exhaust. 
Opening port x admitted steam behind the piston to 



SLIDE VALVE GEARS. 




s 



THE PRIMITIVE ENGINE. 




10 



SLIDE VALVE GEARS, 




THE PRIMITIVE ENGINE. II 

drive it forward, and opening y enabled the steam 
which previously filled the space in front of the piston 
to escape to the cavity z, which communicates through 
the exhaust pipe with the atmosphere or condenser, as 
the case may be. In Fig. 4, the crank shaft has turned 
through an additional angle of forty five degrees, bring- 
ing it at right angles to its initial position. The pis- 
ton is now at the centre of its travel, and the valve at 
its extreme right hand position. As the rotation con- 
tinues, the piston continues to advance ; but the valve 
reverses its motion, and gradually closes its ports, until 
when the crank completes a half revolution, as shown 
in Fig. 5, the valve reaches its middle position at which 
it stood in Fig. 2, with all ports closed. Continuing 
the motion, the valve is carried to the left, opening 
port y to steam and x to exhaust, as shown in Fig. 6, 
and the piston is driven back to its original position ; 
and this sequence of operations will obviously continue 
indefinitely. 

With the eccentric located as in the figures, the di- 
rection of rotation must be as described. This will be 
apparent if, starting with Fig. 2, rotation in the opposite 
direction be imagined. The effect of this would be to 
open port x to exhaust and y to steam, thereby effectu- 
ally stopping the rotation in the direction imagined. 
To effect this reverse rotation the eccentric must be 
located diametrically opposite to the position shown in 
the figures.* The student should satisfy himself of 

* This is true with the primitive form of valve only. With valves 
having lap, as actually used, the eccentric position for reverse rota- 
tion is not diametrically opposite from the position required for for- 
ward rotation. This subject will be referred to again. 



SLIDE VALVE GEARS. 




DEFECTS OF THE PRIMITIVE ENGINE. 1 3 

the correctness of this fact by supposing the eccentric 
so located, and then following the motion through a 
revolution. 

Throughout this book, whether shown or not, it will 
be understood that the cylinder is located as in the 
figures already explained, i.e., to the left of the shaft ; 
and unless otherwise specified, that the direction of 
rotation is the same as in these figures, i.e., " over." 



DEFECTS OF THE PRIMITIVE ENGINE. 

With the construction of Figs. 2-6 the opening and 
closing of the ports are coincident with the passing of 
the centre by the crank. Economy of steam and suc- 
cessful running require that the following changes be 
made in this distribution of the steam : 

I. The opening of the steam port or "admission" 
should occur slightly before the crank reaches the cen- 
tre.* In a general sense this is called giving the valve 
steam lead or simply lead. In a more strict sense, that 
term means the width of opening in fractions of an 
inch which the valve has given to the steam port at the 
instant the crank passes the centre. 

II. The closing of the steam port or " cut-off " should 
occur a good deal before the crank passes the centre. 

III. The opening of the exhaust port or " release," 

* Of late years a difference in practice has arisen in this respect. 
Some makers now set their valves to open the port just as the crank 
passes the centre, and in some cases the admission is delayed until 
after that event. The statement in the text, however, represents 
general practice. This subject will be referred to again farther on. 



14 



SLIDE VALVE GEARS. 



i? 




LAP. 15 

and its closing or " compression," should occur earlier 
than the opening of the steam port, but not so early as 
its closing. As the width of port opening to steam as 
the crank passes. the centre is called steam lead, so the 
width of opening to the exhaust at the same instant is 
called exhaust lead or inside lead (compare page 4). 

These changes in the steam distribution are brought 
about by two changes in the valve gear . (1.) The valve 
is given lap, and (II.) The eccentric is advanced on the 
shaft ahead of the position given. 



LAP. 



Fig. 7 is a reproduction of Fig. 2, with the addition 
of outside or steam lap to the valve. There is no 
change in the exhaust side of the valve nor in the 
angular position of the eccentric, and it is obvious that 
the ports will be opened and closed to the exhaust as 
the crank passes the centre exactly as before ; but the 
port x will not be opened to steam until the valve has 
been carried to the right an amount equal to its lap. 

This will happen as shown in Fig. 8, when the shaft 
has turned through an angle def, such that df, or what 
is the same thing, eg, is equal to the lap. This angle 
def is called the lap angle. The valve opens port x to 
steam when the edge of the valve passes the edge of 
the port going to the right, and it closes it when the 
edge of the valve passes the edge of the port going to 
the left. The position of the valve is the same at clos- 
ing as at opening, the only difference between the two 
acts being in the direction of the valve's motion ; con- 



i6 



SLIDE VALVE GEARS. 




LAP, 



17 




1 8 SLIDE VALVE GEARS. 

sequently the port must close with the eccentric at h, 
vertically below/, as shown in Fig. 9. From this, two 
important and fundamental facts can be learned : 

I. During the time that steam was being admitted 
the eccentric (and with it the shaft and crank) turned 
through the angle fch. Now feh is equal to a semi- 
circle less def and less hei, that is, a semicircle less twice 
the lap angle, and this is the first result of the addition 
of lap to the steam side of the valve. During the 
admission of steam the crank turns through an angle 
equal to a semicircle less twice the lap angle. 

II. In the case of the primitive valve of Figs. 2-6, the 
port began to open with the eccentric in the position of 
Fig. 2. It attained its greatest opening in the position 
of Fig. 4, and the maximum width of port opening was 
equal to the throw of the eccentric. With the valve of 
Figs. 7-9, however, the port does not begin to open 
until the eccentric reaches the point f, and the remain- 
ing travel gk only is available as port opening. This 
width of opening, gk, is equal to ek less eg, that is, to 
the throw of the eccentric less the lap of the valve ; and 
it follows at once that if a valve with lap is to give the 
same port opening as another without lap, the eccentric 
throw of the former must exceed that of the latter, and 
the greater the lap the greater must be the throw. 



ANGULAR ADVANCE. 

The last section has shown how, by the addition of 
lap, the period of port opening may be shortened as 
desired. While, however, the method of regulating 



ANGULAR ADVANCE. 1 9 

the length of period of port opening was pointed out, 
nothing was said about properly timing the opening 
or closing of a valve having lap with reference to the 
position of the piston, and in point of fact in Fig. 8 
the port opening to steam occurred long after the 
crank had passed the centre. The correct timing of 
the events of the stroke, and especially of the admis- 
sion of steam, is obtained by advancing the eccentric 
around the shaft from the position thus far shown. 
In order to give admission to the steam at the instant 
the crank passes the centre, it is necessary to first 
locate the crank on the centre, then to advance the 
eccentric around the shaft such an amount as to 
draw the valve to the right a distance equal to the 
steam lap, and finally to secure the eccentric in that 
position. Such a setting of the eccentric is shown in 
Fig. 10, in which the eccentric has been turned forward 
until the distance df ox its equal, eg, is equal to the lap. 
Such advance of the eccentric on the shaft is called the 
angular advance or the advance angle of the eccentric ; 
and if the admission is to occur with the crank on the 
centre, as in this instance, the advance angle of Fig. 10 
is equal to the lap angle of Fig. 8. Having secured a 
proper admission to the steam, it is proper to inquire 
next into the effect which this change in the angular 
position of the eccentric has had on the other events of 
the stroke. It is sufricientlv obvious that turning- the 
eccentric forward a given angle would simply cause 
each event to occur that much earlier in the rotation 
of the crank. After steam lap had been added, and 
before the advance of the eccentric, the cut-off occurred 
with the crank lacking one lap angle of having reached 



20 



SLIDE VALVE GEARS. 



s 



£ 



I 

I 
i 




LEAD. 21 

the centre (see Fig. 9). Advancing the eccentric one 
lap angle will cause cut-off to occur one lap angle earlier 
still, or with the crank lacking two lap angles of having 
reached the centre. Before the advance of the eccen- 
tric, the opening and closing of the ports to the exhaust 
occurred as the crank passed the centre (see Figs. 5 and 
7). Advancing the eccentric one lap angle swill there- 
fore cause both release and compresssion to occur with 
the crank lacking one lap angle of having reached the 
centre. 

Summarizing then, the valve has had steam lap 
added to it, and the eccentric has been advanced by 
an angle equal to the lap angle, and the resulting steam 
distribution is as follows : Admission occurs as -the crank 
passes the centre ; cut-off occurs two lap angles before 
the centre ; and release and compression occur one lap 
angle before the centre. 

Throughout this book the advance angle will be 
designated on the diagrams by the letter $ (delta). 



LEAD. 

It was explained on page 13 that the admission of 
steam should take place slightly before the crank 
reached the centre, and that such early admission was 
called lead. In the last section, for the sake of sim- 
plicity, the admission was supposed to occur as the 
crank passed the centre. In other words, the lead was 
made zero. It now becomes in order to examine the 
method for the introduction of lead, and the changes 
in the other events of the stroke which follow. In Fisr. 



22 



SLIDE VALVE GEARS. 



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LEAD. 33 

10 the eccentric was advanced to cause admission to 
occur on the centre. If it is proposed to give the valve 
lead, the eccentric must be advanced still further, so as 
to draw the valve to the right an additional amount 
equal to the lead desired. In Fig. 11 this additional 
advance has been made, the eccentric having been 
moved from /of Fig. 10 (reproduced in Fig. 11) to /. 
The angle fel is called the lead angle, and it follows that 
in all cases the angular advance is equal to the lap angle 
plus the lead angle. If the lead is zero, then, as be- 
fore found, the angular advance is equal to the lap an- 
gle. If in Fig. 1 1 the crank shaft be turned backward, 
the valve will close the port when the eccentric reaches 
point f and the crank stands at m, the angle nem being 
equal to the angle/*?/. In other words, the lead angle 
is equal to the angular distance which the crank lacks 
of having reached the centre when admission occurs. 

It was found on page 19 that advancing the eccentric 
on the shaft a given angle advanced all the events of 
the stroke correspondingly, and the resulting distribu- 
tion of steam with no lead was summarized on page 21. 
If now the valve have lead so that the angular ad- 
vance be greater than the lap angle, the steam dis- 
tribution given on page 21 is changed as follows: 

Admission occurs with the crank lacking the lead 
angle of having reached the centre. 

Cut-off occurs with the crank lacking two lap angles 
and one lead angle of having reached the centre. 

Release and compression occur with the crank lack 
ing one lap angle and one lead angle of having reached 
the centre. 

An application of the above principles is all that is 



24 



SLIDE VALVE GEARS. 



necessary for the analysis of the steam side of any exist- 
ing plain slide valve, as will be seen from the following 
example : 

An eccentric has a throw of if " , the valve has one- 



e m 




Fig. 12 



inch steam lap, no exhaust lap, and the eccentric is set 
to give^Jg-" lead. Required the greatest port opening, 
and the crank positions for admission, cut-off, release, 
and compression. 

In Fig. 12 strike the circle with a radius equal to the 



EXHAUST LAP. 25 

throw of the eccentric, and lay off Oa equal to the lap 
of the valve and a b equal to the lead. Erect perpen- 
diculars from points a, b, giving points c, d. Now eOc is 
the lap angle, cOd is the lead angle, and eOd is the an- 
gular advance. Lay off fg equal to cd, giving Og the 
crank position for admission. Make hi equal to twice ec 
plus cd, giving the crank position Oi for cut-off. Make 
kh equal to ec plus cd, giving Ok the crank position for 
release and compression. Finally, ah is the greatest 
steam port opening. 

The student should familiarize himself with the prin- 
ciples thus far treated, by the solution of a variety of 
problems similar to the following : 

Problem I. Eccentric throw if, lap f, lead ^ Re- 
quired crank positions for lead, cut-off, compression and 
release, and port opening to steam. 

Problem II. Eccentric throw if, lap -J-J, lead 3%-. Re- 
quired as before. 



EXHAUST LAP. 

The addition of lap to the inside of the valve has the 
same effect upon the opening and closing of the port 
to the exhaust that steam lap has upon opening and 
closing it to steam, i.e., it delays the opening and 
hastens the closing, and it delays the opening and has- 
tens the closing by an angle of rotation of the crank 
equal to the exhaust lap angle — that angle being found 
exactly as was the steam lap angle in Figs. 8 and 12. 
Returning to Fig. 12, if the valve were to have an ad 
dition of -§• inch inside lap, its effect upon the release 



26 SLIDE VALVE GEARS. 

and compression could be found as follows : Make 01 
equal the inside lap, and by the line Im find the exhaust 
lap angle eOm. From k lay off em both upward and 
downward. Draw the radii On and Op, and the results 
are On for the crank position at release, and Op for com- 
pression. It is unnecessary to go in detail through the 
results following the introduction of negative inside 
lap. It will be seen at once that its results are the di- 
rect reverse of the preceding, i.e., to hasten the opening 
and delay the closing of the ports. If in the illustration 
preceding, the valve had been given -J negative inside 
lap, the crank positions found for release and compres- 
sion would have changed places. 

It was shown on page 18 that the steam port open- 
ing given by a valve having steam lap is equal to the 
throw of the eccentric less the steam lap, and it follows 
by the same course of reasoning that the exhaust 
opening is equal to the throw less the exhaust lap. 
Since the exhaust lap is always less than the steam lap, 
it follows that the port opening to exhaust is always 
greater than to steam. 



BACKWARD ROTATION. 

It was explained on page 1 1 that with a primitive 
valve the eccentric location for rotation in the reverse 
direction would be diametrically opposite that shown 
in Figs. 2-6. For a valve having lap, the position for 
reverse rotation is found by laying off the advance 
angle in the direction of the proposed rotation from the 
position for a primitive valve. The effect of a rock 



BACKWARD ROTATION. 27 

shaft in the valve motion (for an example of which see 
any American locomotive) is to reverse the motion of 
the valve as compared with the eccentric, and hence to 
require a location of the eccentric which will provide 
for this reversal. The position of the eccentric for 
either direction of rotation, and with or without a rocker, 
may be located from the following facts : 

I. Without a rocker the eccentric for a primitive 
valve is 90 in advance of the crank in the direction 
of the rotation. With a rocker the eccentric is behind 
the crank. 

II. The advance angle is laid off in all cases in the 
direction of the rotation from the position for a primi- 
tive valve. 

One qualification should be added to the above, as 
follows : In all the cases thus far shown, the location of 
the eccentric for the primitive valve is as stated at right 
angles to the crank. In certain cases, owing to the 
character of the connections between the eccentric and 
valve, this is not true. For an example see Figs. 58 
and 59. In cases of this kind the location of the ec- 
centric can be found as follows : Carry the centre of 
the eccentric strap to the centre of the crank shaft. 
Through the centre of the shaft draw a line perpen- 
dicular to the location of the eccentric rod thus found. 
This perpendicular gives the location of the eccentric 
for the primitive valve, and the angular advance is to 
be laid off from it in the direction of the rotation. 



28 SLIDE VALVE GEARS. 



THE BILGRAM DIAGRAM. 



Any existing slide valve can be analyzed by the 
methods that have been followed in explaining the 
action of the valve, and new valves could be designed 
by a tentative application of the same methods. Such 
a plan of procedure, however, would be exceedingly 
tedious, and much ingenuity has been expended in de- 
vising briefer and better methods. Of these, by far 
the best is the diagram devised by Mr. Hugo Bilgram, 
and explained below. The chief office of such a dia- 
gram is to show briefly and accurately the position of 
the valve for any and every position of the crank. 

A 





Fig. 13 

The demonstration of the Bilgram diagram depends 
upon the following theorem of geometry : In Fig. 13 
let ABC and abc be two triangles, such that any two 
of their angles, as those at A y C and a, c, and any one 
side, as BC and be, are respectively equal. Then this 
theorem asserts that all of the other parts of the tri- 
angles are equal, i.e., angle B to b, side AC to ac, and 
side AB to ab. 

In Fig. 14 let A be the dead-point location of the 
crank, and B be the corresponding position of the ec- 



THE BILGRAM DIAGRAM. 



2 9 



centric centre, S being the angle of advance. It is 
obvious enough that the valve is now located a dis- 
tance Bb (equal to the sum of the lap and lead) to the 
right of its middle position. Imagine the crank to 
turn through the angle ^toa new position A' . The 
eccentric will turn through an equal angle a to its new 




Fig- 14 



position B', and the valve will then be located a dis- 
tance B'b' to the right of its middle position. Lay 
off the angle 8 upward from OX, and thus locate a 
fixed point, Q. From Q drop Qq perpendicular to the 
new crank position extended. There are thus formed 
two triangles, B'b ' and QqO, and in them B'O equals 



30 SLIDE VALVE GEARS. 

Q0, since both are radii of the same circle. Angles 
B'b'O, QqO are equal, because both are right angles; 
and finally, angle B' Ob' equals QOq, since each is equal 
to 6 plus a. The two triangles have thus two angles 
and a side of one, respectively equal to two angles and 
a side of the other, and it follows that the triangles are 
equal in all their parts, and hence Qq equals B'b '. B'b' 
is the distance which the valve has travelled from its 
central position for crank position A\ and it hence 
follows that Qq likewise equals that distance. The 
same demonstration can be made for any other crank 
position as well as for A' ', and the following general 
fact is thus established : Lay oft' the advance angle 
above the centre line, and thus locate the fixed point 
Q. Draw any crank position desired, and extend it if 
necessary. From the fixed point Q drop a perpendic- 
ular to the crank line, and the length of the perpendic- 
ular will be equal to the distance of the valve from its 
central position for the crank position taken. For ro- 
tation in the reverse direction, points B and Q would fall 
below instead of above the centre line. 

The length of the perpendicular Qq gives the dis- 
tance of the valve from its central position, but it does 
not of itself show whether the valve is located to the 
right or to the left of its middle position. That fact 
will be determined instinctively after a little practice 
in the use of the diagram ; but if desired it can be 
determined by the following consideration : Referring 
to Fig. 14, that side of the crank and of its imaginary 
extension facing the space toward which the crank is 
revolving may be called the face side of the crank, and 
the opposite side may be called the rear side. If the 



THE BILGRAM DIAGRAM. 3 1 

perpendicular Qq falls upon the face side of the crank, 
the valve is to the right of its middle position ; if the 
perpendicular falls upon the rear side, the valve is to 
the left of its middle position.* As has been explained, 
the greatest port opening is equal to the throw of the 
eccentric OQ, Fig. 14, less the lap ; and it is also true 
that for any position of the crank, the port opening 
which exists at that position is equal to the displace- 
ment of the valve from its central position less the lap, 
i.e., to the value of Qq for that position, less the lap. In 
other words, if for any crank position the value of Qq 
be found, and from it the steam lap be taken, the result 
will be the distance which the steam port stands open for 
that crank position. If, on the other hand, the exhaust 
lap be taken from it, the result will be the distance which 
the exhaust port stands open. This subtraction can 
be conveniently made by striking two circles L, I from 
Q as a centre, and with radii equal to the steam and 
exhaust laps respectively, as is done in Fig. 15. In 
case the inside lap is negative, it of course increases 
instead of decreases the port opening to exhaust. 
Throughout this book, positive lap will be shown by 
full circles, and negative lap by dotted circles. 

Starting with the position A, Fig. 15, the length of 
the perpendicular which locates the valve is Qq y and the 
width of opening of the port to steam is aq ; A being 
the dead-point position of the crank, aq is the lead of 
the valve. Similarly, bq is the exhaust lead. In Fig. 16 
the valve is shown in position for crank position A. 



* This takes it for granted, as explained on page 13, that the posi- 
tion of the cylinder is to the left of the shaft. 



32 



SLIDE VALVE GEARS. 



The opening of the port c to steam is equal to aq of 
Fig. 15, and the opening of port d to exhaust is equal 
to bq. Similarly, the displacement e of the valve from 
its centre is equal to Qq* As the crank revolves, Qq 
gradually lengthens until the crank reaches position B 
perpendicular to OQ, when Qq becomes QO, which is its 




greatest value. The valve now stands at its extreme 
right hand position as shown in Fig. 17, the ports being 
open to their greatest amount — the steam port by a 



* It will be understood that the distances stated as equal are not so 
shown in the cuts, as they are necessarily drawn to different scales. 



THE BILGRAM DIAGRAM. 



33 



width a'O, and the exhaust port b'O. Passing B, the 
valve returns towards its central position, and at C the 




Fig. 16 

displacement has been reduced to equality with the 
steam lap. The port c is therefore closed to steam, and 




cut-off takes place as shown in Fig. 18. At D, port d 
is closed to the exhaust, Fig. 19, and compression be- 




Fig. 18 

gins. At F, port c is opened to exhaust, Fig. 20, and 
release occurs. At G the valve is ready to open port 
d for the return stroke, Fig. 21 ; and at H the valve has 



34 



SLIDE VALVE GEARS. 



opened port d by the amount of the lead. The posi- 
tions of the crank for the return stroke are readily found 




Fig. 19 

by extending the crank lines beyond the centre. Thus 
I is the lead position, K the release, iJ/ the compression, 




Fig. 20 

and iVthe cut-off. Had there been no exhaust lap, re- 
lease and compression would have occurred simultane- 




Fig. 21 

ously at E ; and had the exhaust lap been negative, re- 
lease and compression would have exchanged places, 
and the maximum opening to exhaust would have been 
Ob". 



THE BILGRAM DIAGRAM. 35 

Consideration of this diagram will recall and enforce 
the essential effect of lap, as stated on page 18 ; i.e., to 
shorten the period during which the port is open. Thus 
with steam lap the steam port is open when the crank 
is moving from /to C and from G\.o N, and with exhaust 
lap the exhaust port is open from K to D and from F 
to M. With negative inside lap, on the other hand, 
the port is open during more than half a revolution, 
i.e., from M to F. 

The principles laid down should be fixed in the mind 
by the solution of practical problems similar to the 
following : 

Problem III. Throw of eccentric 2", steam lap if, 
exhaust lap J, lead \. Required port opening and 
points of cut-off, release, and compression. 

Problem IV. Travel of valve 3", steam lap j-, nega- 
tive exhaust lap T \, lead \. Required as in the last 
problem. 

This diagram is of use not only in analyzing existing 
valve motions as in the preceding problems, but also in 
designing new ones to meet required conditions. The 
method of using it for this purpose is best shown by an 
illustrative example, as follows : 

The valve for a certain engine is to have a steam- 
port opening of f", a lead of y 1 ^ ; is to cut off the steam 
at J of the stroke, and open the exhaust at 95 per cent 
of the stroke. Required the inside and outside lap, the 
throw and advance angle of the eccentric, and the point 
of exhaust closure. 

In Fig. 22 make AB equal to the length of the stroke, 
using a scale of three inches to the foot. Make Aa 



36 



SLIDE VALVE GEARS. 



equal f of AB, and Ab equal .95 of y4i?. Draw the 
semicircle A'a'b'B' to represent the path of the crank, 
and project to it the points a, b. Draw Oa' and Ob' , 
which are the crank positions for cut-off and release. 
Draw cd such that de is equal to the lead opening, -^ 




Fig. 22 



inch ; and strike the arc fg with radius equal to the 
port opening. Find by trial the centre and radius of 
the steam lap circle such that it shall be tangent to 0a\ 
cd, and fg. From the same centre strike the exhaust 
lap circle tangent to Ob' . Draw Oh! tangent to the ex- 
haust lap circle and project h' to the stroke line, giving h. 



THE BILGKAM DIAGRAM. 



37 



Measuring the diagram, the results sought are, outside 
lap y^ inch, inside lap J inch, throw of eccentric i T \ 
inch, advance-angle iOB' , point of exhaust closure h, 
which is 90 per cent of the stroke. It may be observed 
further, that the exhaust port opening is Ok ; in this 




case and in all others this is more than sufficient for 
the purpose, and hence no particular care is necessary 
in relation to it. 

An interesting and profitable exercise in this connec- 
tion is to make a diagram showing by a continuous line 
the varying width of port opening throughout the 
stroke. This is illustrated in Fig. 23, in which the con- 
tinuous base line represents the stroke of the piston of 
Fig. 22 divided into tenths. At each division a per- 
pendicular is erected, and on this perpendicular is laid 
off the opening of the ports to steam and exhaust for 
that position of the piston — this opening being obtained 



from Fig. 22. 



Through the points thus found the 



3 8 SLIDE VALVE GEARS. 

curved lines are drawn-the upper one for the exhaust 
port and the lower one for the steam port. The cross- 
ing of the base line by the curved lines shows the points 
c/cutting off and compression, respectively ; and the 
extension of the curved lines below the base line shows 
the distances by which the edges of the valve have 
closed the ports. This diagram shows at a glance how 
gradual is the cutting off of the steam. Such diagrams 
are exceedingly useful in connection with the study of 
independent cut-off valves, many of which will not give 
flattering results when subjected to this analysis. 

LAYING OUT THE SLIDE VALVE. 
The diagram Fig. 22 gives all the dimensions neces- 
sary for laying out its valve, except the width of the ex- 
haust cavity, and that is determined at once by draw- 
ing the valve and its seat with the valve at one extreme 
of its travel, that is, in the position already shown in 
Fig 17. Referring to Fig. I, it is clear that the width 
of the acting face of the valve is equal to the outside 
lap plus the width of the port plus the inside lap. In 
order to determine all the dimensions of the valve face 
and seat proceed as follows : Lay down the width of 
the left hand port (rules for which will be given farther 
on) and the width of the bridge (usually made equal to 
the thickness of the cylinder). On these locate the 
actin- face of the valve with the port open to steam to 
the greatest amount intended. From the exhaust 
edge of the acting face lay off the distance /, Fig. 17, to 
equal or slightly exceed the width of the port, thus com- 
pletely determining the exhaust cavity in the cylinder. 



VELOCITY OF THE VALVE. 39 

From the right hand edge of this cavity the remaining 
bridge and port are to be laid off the same as the 
left hand side. The valve seat being completed, and 
the steam and exhaust laps being known, it is easy to 
complete the drawing of the valve. The proper deter- 
mination of the distance/, Fig. 17, as above, is all that 
need be considered in designing the exhaust cavity in 
the cylinder. If this cavity be made too narrow, it will 
cramp the exhaust ; if too wide, it will add unnecessari- 
ly to the size of the valve and to the steam pressure 
upon it, and hence to the friction and wear and tear on 
all the valve gear. Further than this, the size of the 
exhaust cavity has no influence on the valve motion. 

It will be observed that in the valve diagram Fig. 22, 
the lines for the piston and crank circle are drawn to a 
reduced scale, but the lines for the valve and eccentric 
are full size. The reduced scale for the crank dimen- 
sions is for convenience. The valve dimensions should 
always be made full size. 

* VELOCITY OF THE VALVE. 

Referring to Fig. 14, it is obvious that the valve 
will move with its greatest velocity when the eccentric 
is at P. At this point its velocity may be represented 
by the eccentric throw OP. At any other position of the 
eccentric as B, the valve will move with a velocity pro- 
portional to the leverage with which the eccentric acts 
upon it, that is, Ob. Similarly at B' the velocity of the 
valve will be represented by Ob' . In the original dem- 
onstration of this diagram it was shown that the tri- 
angles B'b'O and QqO are equal in all their parts. It 



40 SLIDE VALVE GEARS. 

hence follows that Oq equals Ob' . In other words, if a 
perpendicular be drawn from the point Q to any crank 
line, the distance from the centre of the shaft to the 
foot of that perpendicular will represent the velocity 
with which the valve is moving with the crank in that 
position. Quick closure of the port in cutting off steam 
is considered a merit in a valve motion, and this prop- 
erty of the Bilgram diagram furnishes a ready means 
of comparing the merits of different valve gears in this 
respect. In Fig. 15 the perpendicular Qc will deter- 
mine the distance Oc, which represents the velocity 
with which the valve is moving at the instant of 
cutting off. 

LIMITATIONS OF THE PLAIN SLIDE VALVE. 

Careful study of the Bilgram diagram will explain 
the features of the common slide valve which have usu- 
ally been considered to limit its application to cases 
where a comparatively late cut-off was to be employed. 
Thus, in the example of Fig. 22, let the given condi- 
tions be the same, except that cut-off is to be at half 
stroke instead of three quarters, and let there be no 
inside lap. The results are shown in Fig. 24, where 
it will be seen that the throw has increased to two 
inches and the steam lap to one and three eighths 
inches, while the common point of compression and re- 
lease has gone back to bh — 85 per cent of the stroke. 
At still earlier points of cut-off these features become 
still more marked, the travel of the valve rapidly in- 
creasing and the release and compression becoming 
more and more premature. The increased lap and 
travel increase directly the size and duty which the 



LIMITATIONS OF THE PLAIN SLIDE VALVE. 41 

parts have to perform. Further, as will be seen by re- 
ferring to the section on laying out the slide valve, 
and to Fig. 17, they increase the size of the exhaust 
cavity, and so add to the size of the valve and to the 
steam pressure upon it. The release can be made later 




Fig. 24 



by the addition of exhaust lap, but this involves a still 
earlier compression. From these considerations it has 
been generally held and taught that the plain slide 
valve could not be profitably employed for cut-offs 
shorter than one half or five eighths stroke. The 



42 SLIDE VALVE GEARS. 

methods which have been adopted to overcome the 
above difficulties will form the subject of a later chapter, 



THE AREAS OF THE PORTS AND PIPES. 

It will be seen from the foregoing that the width of 
port opening is an essential factor in the design of a 
valve motion. The exact meaning of the term port 
opening in this connection should be clearly under- 
stood. By that term is to be understood the extreme 
distance of the steam edge of the valve from the steam 
edge of the port. This distance may, and often does, 
exceed the width of the port — that is, the valve may 
have over-travel to secure certain real or fancied advan- 
tages. In engines with fixed eccentric, which are now 
under consideration, the only benefit of such over-travel 
is to increase the sharpness of the cutting off. This, in 
the author's opinion, is not worth its cost, and hence he 
does not practise nor recommend it. In locomotives 
and shifting eccentric engines the travel of the valve is 
shortened at the early cut-offs, and in such engines, in 
order to secure sufficient port opening at the early cut- 
offs, it is proper and necessary to give over-travel at the 
late ones. 

It is clear that the area of the port opening should 
have a proper relation to the size and speed of the en- 
gine. It will be furthermore clear without extended 
explanation, that in engines having separate admission 
and exhaust ports (for example, the Corliss) the exhaust 
passage should have a greater area than the admission 
passage. In engines using the same passage for both 
purposes, to which this book relates, that passage 
should be proportioned to meet the requirements of 



THE AREAS OF THE PORTS AND PIPES. 



43 



the exhaust, and then, if desired, it need not be opened 
to steam any wider than is necessary for its use as a 
steam port, 

In determining the area of a pipe or passage it is 
treated as though the velocity of the steam through it 
were equal to the velocity of the piston multiplied by 
the ratio of the area of the piston to the area of the 
port or pipe. Of course, owing to the expansion of 
the steam at release, this is not strictly true, but it 
simplifies the determination of the dimensions, and as 
long; as the rules and tables make allowance for its lack 
of precision, the results are the same as though a more 
complicated process were gone through. 

As the result of experience and experiments, the 
proper velocities of the steam through the various pas- 
sageways are as follows : 

Through the steam pipe 8000 feet per minute. 

Through the exhaust port 6000 feet per minute. 

Through the exhaust pipe 4000 feet per minute. 

For free admission of steam the port should be opened 
three fourths of its width. From the above data the 



following table is constructed for convenient use : 


Piston Speed, 
Feet per Minute. 


Diameter of Steam 


Diameter of Exhaust 


Area of Exhaust 


Pipe (Diameter of 
Piston = 1). 


Pipe (Diameter 
of Piston = 1). 


Passage (Area of 
Piston = 1). 


200 


-158 


.223 


•033 


250 


,176 


.248 


.042 


300 


.194 


272 


.050 


350 


.209 


.294 


.058 


400 


.224 


•314 


.067 


450 


•237 


•333 


•075 


500 


.250 


• 353 


.083 


550 


.260 


.368 


.092 


600 


.274 


•385 


. IOO 



44 SLIDE VALVE GEARS. 

The table determines the diameters of the steam 
and exhaust pipes at once, but it gives the area only 
of the port, leaving its length and breadth to be de- 
termined by the designer. The practice in this par- 
ticular is very diverse. In shifting eccentric automa- 
tic engines, which form the subject of Part II, and in 
which every expedient must be employed to secure 
sufficient port opening, the length of the ports is often 
made to equal or even exceed the diameter of the cyl- 
inder; but in plain slide valve engines of the usual type, 
a length of about three quarters the cylinder diameter 
more nearly represents average practice. This length 
determined, it is only necessary to divide the area of 
the passage by it to determine the width of the port, 
and three fourths of this will give the port opening to 
be used in laying out the diagram. 

A " rule of thumb" which is in very common use is 
to make the steam pipe one fourth the diameter of the 
cylinder, and the exhaust pipe one third. At slow 
speeds this rule gives an excess of capacity over the re- 
quirements, to which of course there is no objection; 
but at high speeds it gives a deficiency. On high grade 
engines, where the best results are sought, steam pipes 
are seen as large as one third and exhaust pipes one 
half the cylinder diameter. 

All the principles thus far given will be found re- 
quired in the solution of the following 

Problem V. — An engine with a 10" X 1 5" cylinder 
is to run at 200 revolutions per minute. Cut-off is to 
be at f stroke, release at .93 stroke, and lead is to be ^\". 
Required the diameters of steam and exhaust pipes, the 



ANGULAR VIBRA TION OF THE CONNECTING ROD. 45 

dimensions of the ports, the travel, and the steam and 
exhaust laps of the valve. 

* THE ANGULAR VIBRATION OF THE CONNECTING ROD. 

As has been explained, the slotted cross-head was 
adopted in the preceding to avoid certain distortions 
which are incident to the use of the connecting rod. It 
is now proper to discuss these distortions, and explain 
the methods for neutralizing their effects. 

With the slotted cross-head the position of the piston 




Fig. 25 



\c 



or cross-head in its stroke for any crank position is found 
by simply projecting the crank position to its horizontal 
diameter, or a line parallel thereto, by means of a straight 
projecting line, as was done in Figs. 12, 22, and 24. Fig. 
25 is a skeleton diagram of the usual connecting rod 
and crank. It is obvious that if the crank pin end of 
the connecting rod be disconnected from the crank pin 
and carried to the centre of the crank shaft the cross- 
head pin will occupy its central position a. If from 
this position the crank pin end be carried to either 
" quarter" position of the crank pin b, c, the cross-head 



46 SLIDE VALVE GEARS. 

pin will be drawn toward the shaft and will occupy the 
position d. For the forward stroke the position of the 
cross-head is measured from e as a starting point, and 
hence the cross-head and piston have moved too far 
by the distance ad. For the return stroke the position 
is measured from /asa starting point, and hence the 
cross-head and piston have not moved far enough by 
the same distance. If the valve motion were laid out 
by the preceding methods to cut off steam at half stroke, 
it would in fact cut off later than half stroke for the 
forward stroke and earlier for the return. The same 
distortion takes place at all other positions of the crank 
except at the centres, though to a less degree ; and it 
follows that all the events of the stroke except the lead 
occur too late in the forward stroke and too early in 
the return. The amount of this distortion can be found 
for any position of the parts, as is done in Fig. 25, for 
the position shown, by striking an arc with radius equal 
to the length of the connecting rod, the distance gh be- 
ing equal to ad. Striking this arc is, in fact, projecting 
the point b to the centre line with the circular arc in- 
stead of a straight line, as has heretofore been done ; 
and in order to find the true relation between the posi- 
tions of the piston and crank, it is only necessary to 
project the one to the other by means of such circular 
arcs with radius equal to the length of the connecting 
rod. It is often convenient to measure the piston posi- 
tions for the forward and return strokes from the same 
starting point as z, and in order to do this it is only 
necessary to strike the arcs for the forward and return 
strokes from opposite sides of the shaft. Thus, with 
the crank on the quarter, the piston will have moved 



ANGULAR VIBRA TION OF THE CONNECTING ROD. 47 

through the distance ih for the forward stroke and ik for 
the return. Similarly, if the crank move through an angle 
ibl for the forward' stroke, the piston will have moved 
through the distance io ; and if the crank move through 
the same angle from p on the return stroke the piston 
will have moved through the distance iq. The directions 
of these distortions for the two strokes are best distin- 
guished by remembering that the effect of the connect- 
ing rod is always to draw the piston too near the crank. 

The amount of these distortions will diminish if the 
length of the connecting rod be increased, and if a con- 
necting rod of infinite length be conceived, the distor- 
tions will disappear. Hence a piston motion without 
distortion, such as is given by the slotted cross-head, is 
often called the motion due to a connecting rod of in- 
finite length. 

Since the speed of the crank's rotation is uniform, 
and the piston must travel farther for a given angle of 
crank rotation in the forward than in the return stroke, 
it follows that the speed of the piston's motion is greater 
in the forward than in the return stroke. 

These principles can be applied to the problems al- 
ready given, and thereby determine the actual positions 
at which the various events occur. Fig. 26 is a repro- 
duction of Fig. 22, but with the projections made by 
circular arcs instead of straight lines. It thus appears 
that with the valve there designed, the cut-off, instead 
of taking place as intended in Fig. 22, will really take 
place after a piston travel Aa r , Fig. 26, in the forward 
stroke and A a" in the return. Similarly, the compres- 
sion will take place after travels Ah' and Ah", and the 
release after Ab' and Ab" . If preferred, the construe- 



4 3 



SLIDE VALVE GEARS. 



tion may be made by repeating the lap circles below 
the centre line in position for the return stroke, as is 




Fig. 26 



done in Fig. 27. With this construction the measure- 
ments are necessarily made from A for the forward 
stroke and B for the return. Of these two plans that 
of Fig. 26 possesses the advantage that it shows at a 
glance the difference between the points of cut-off, etc., 
in the two strokes. 

Problem VI. It is required to find the true positions 
for cut-off, release, and compression of the valve of 



ANGULAR VIBRATION OF THE ECCENTRIC ROD. 49 




Fig. 27 

Problem III. Length of connecting rod five times the 
crank. 



* THE ANGULAR VIBRATION OF THE ECCENTRIC ROD. 

As has been explained, the eccentric is in effect a 
crank and the distortions introduced by the connecting 
rod into the motion of the piston are likewise intro- 
duced by the eccentric rod into the motion of the valve. 



SO SLIDE VALVE GEARS, 

In other words, if the distortions are not corrected, the 
valve, like the piston, will always be too near the crank. 
The throw of the eccentric is much less than the arm 
of the crank, and the eccentric rod is proportionately 
longer than the connecting rod ; hence the distortions 
in the positions of the valve are absolutely and relatively 
smaller than those in the positions of the piston. Since 
the effect of these distortions is to draw the valve too 
near the crank, it follows that if they are not prodded 
for, the lead of the valve at the back end f of the cylinder 
will be increased and for the front end diminished. The 
greatest port openings are measured with the eccentric 
on the centre line of the engine, when these distortions 
vanish ; and hence the two port openings will be equal. 
It is important that the lead openings be equal, while 
it is not particularly important that the maximum port 
openings be equal, provided the smaller one be large 
enough. Hence in practice the eccentric rod or valve 
rod is slightly lengthened to give equal lead at the two 
ends, and the result is that the port opening is slightly 
diminished for the forward stroke and slightly increased 
for the return. This lengthening of the eccentric rod 
is effected in setting the valve for equal lead, and it 
practically corrects the effects of the angular vibration 
of the eccentric rod. 

* EQUALIZED EXHAUST. 

As has been explained, the setting of the valve for 
equal lead practically neutralizes the effect of the an- 

f With apologies to the locomotive fraternity, the end of the cylinder 
farthest from the crank will be called the back end. 



EQUALIZED EXHAUST. 



51 



gularity of the eccentric rod. Nothing, however, has 
yet been done toward correcting the irregularities due 
to the connecting rod, and that is the next subject to 
be discussed. 

If the valve has no inside lap, compression and re- 













^•"^ 




/ 


\ 


/ 


\ 


/ ^" 


^"* — S**^ \ ""^"s. 


/ y 






/ \ >° \ 


/ / 


/ \ s^/^ \ 


/ 


1 J^^s 1 1 \ 1 


/ / 


S / s<Zj>I " \ 


/ / 
/ / 

/ / 


\r \ ' V 




, / 






/ 




1 h \ 


/ \\ 1 




\a j 


*/T\ ^\y 




A » \^^\ 


/ / 


/ / 


I )k^\ ) 


/ / 


/ / 




/ / 


\ \ \ / 






■>««, 


^.^ 







Fig. 28 

lease are coincident, and the correction of one will like- 
wise correct the other. It is desired to cause both these 
events to occur earlier in the forward stroke and later 
in the return stroke, and to accomplish this, it is only 
necessary to give an appropriate exhaust lap to the end 
of the valve nearest the crank shaft, and an equal nega- 



52 



SLIDE VALVE GEARS. 



tive exhaust lap to the other end. In applying this cor- 
rection, it should be remembered that the Bilgram dia- 
gram gives the true relation between the positions of 
the crank and eccentric, and that the distortions under 
discussion are given to the piston through the connect- 
ing rod. In Fig. 28 it is proposed to correct the release 
and compression of the valve shown, which, in the first 
instance, has no exhaust lap. By the vertical projec- 
tion lines the points of release a, b are found in the usual 
way, and by means of the curved projection lines points 
a', b'a.re found for the correct crank positionscorrespond- 
ing to piston positions #, b. If the release and compres- 
sion are to take place at piston positions a, b, they must 
take place at the crank positions a', b' . Drawing the 
crank lines a'Oand b'O, it is easy to add the exhaust lap 
circles shown, from which measurement shows that for 
that edge which effects exhaust at a' a positive lap of 
Jg-" is required, and for b' a negative lap of the same 
amount. The resulting valve is shown in Fig. 29. Had 




Fig, 29 

the valve originally possessed exhaust lap, as in Fig. 
30, exact equalization would have been impossible, al- 
though a result could have been reached sufficiently near- 
ly correct for all practical purposes. The piston positions 



EQUALIZED EXHAUST. 



53 



ior compression a, b and releasee, d are projected to the 
crank circle by circular arcs, as shown, giving the corre- 
sponding crank positions a! , b\ c' , d '. It is apparent at 
once that the change of lap to give compression at a/ is 
greater than the change to give release at d ', and simi- 




Fig. 30 



larly for c' and b' . In such a case the best that can be 
done is to divide the difference, making the alteration in 
the lap halfway between that called for by a' and d' for 
their end of the valve, and half way between that called 
for by c' and b' for their end of the valve. This sub- 
ject wiM be returned to at the close of the next section. 



SLIDE VALVE GEARS, 



EQUALIZED CUT-OFF. 



It was shown in the last section that by introducing 
inequality in the inside laps, the inequality of release 
or compression could be equalized — a change in one 
event being, however, accompanied by a change in the 
other. It is obviously possible to equalize the cut-off 
in a similar manner by making the outside laps un- 
equal. As a change in the inside laps involved both 
release and compression, so will a change in the outside 
laps involve both admission and cut-off ; and since the 
valve, as thus far described, gives equal lead at the two 
ends of the cylinder, it follows that increasing one lap 
and decreasing the other would result in an unequal 
lead — in other words, cut-off equalized by such a 
method would involve unequal lead. Such a method 
is usually explained in detail in books of this character. 
Equality of lead is, however, of more importance than 
equality of cut-off, and hence the method is of no prac- 
tical importance, and is not introduced here. 

The following method f secures equality of cut-off 
without affecting the equality of the lead. It has 
no objectionable features, and is of general utility. 
Throughout the discussion, one fundamental fact must 
be kept in mind, viz. : The acts of opening and closing 
a port by a slide valve differ only in the direction of 
motion of the valve. The port is opened or closed, as 
the case may be, by the edge of the valve passing the 

f First published by the author in the American Machinist for 
March 14, 1889. It was invented independently by Professor Sweet 
and the author, — first, however, by the Professor. 



EQUALIZED CUT-OFF. 



55 



edge of the port, and the position of the valve when 
cut-off takes place is the same as when admission takes 
place. Since the- valve is mechanically connected to 
the eccentric rod pin, it follows that the position of that 
pin must be the same at cut-off as at admission. 

Let it be proposed to design a slide valve to cut off 
steam at half stroke, with equal lead and cut-off. 




First design the valve by the methods already ex- 
plained, then strike the crank and eccentric circles of 
Fig. 31.* Locate points A, B, the positions of the crank 
pin for admission of steam, and the corresponding 
positions a, b for the eccentric centre. With radius 
equal to the length of the connecting rod, and with 

* In this and the following diagrams the throw of the eccentric is 
made disproportionately large, and the eccentric rods disproportion- 
ately short, to add to the clearness of the constructions without un- 
necessarily large diagrams. This gives the appearance of a distorted 
valve movement ; but with working proportions these apparent dis- 
tortions are no greater than with the usual construction, and are not 
objectionable. 



5 6 SLIDE VALVE GEARS. 

centre at the middle position of the cross-head pin, 
strike arcs cutting the crank circle at c and d. Before 
cut-off in the forward stroke, the crank shaft, and with 
it the eccentric, must turn through the angle Ac, and 
in the return stroke Bd. Space off a ' e equal to Ac, 
and b'f equal to Bd. Draw eg and fg, and we have 
point h, where the eccentric centre must be for cut-off 
at c, and i where it must be for cut-off at d. With 
radius equal to the length of the eccentric rod, and with 
centres at b, i> strike arcs meeting at k, and with same 
radius and centres a, h, strike arcs meeting at /. Now 
for admission at A and cut-off at c, the eccentric rod pin 
must be in the same position, and as the eccentric rod 
is of fixed length, this position must be /, that being 
the only point whose distance from both a and h equals 
the length of the eccentric rod. Similarly for admission 
at B and cut-off at d, the pin must be at k. The pin 
can be brought to these positions at the proper time by 
introducing a rock shaft in the valve motion having its 
centre at any point o ; such that an arc struck from it 
shall pass through k and /, and then connecting the 
eccentric rod to it as shown. The valve stem should 
then be connected to the rocker, as shown at m, n. 
The eccentric rod positions for crank positions A, B 
are shown at a/, bk. The rocker fulcrum might be 
located above the centre line, if preferred, at o' . 

In cases where the valve chest is located on the top 
of the cylinder, a rocker of different type, with the arms 
on opposite sides of the fulcrum, becomes necessary. 
The construction for this type of rocker is essentially 
the same as shown in Fig. 32, which is lettered to cor- 
respond with Fig. 31. Of course, with this type of 



EQUALIZED CUT-OFF. 



57 



rocker the eccentric positions a, b change places as 
shown. One result of the equalization growing out of 
the inequality of the rocker arms is to alter the port 
opening from that determined upon in the original de- 
signing of the valve. The motion as thus far deter- 
mined should therefore be treated as a trial result only, 
and the dimensions of the valve and eccentric should 
be altered in the light of the experience gained. 




At the close of the description of Fig. 31 it was 
stated that the rocker fulcrum might be located indif- 
ferently at either or 0' of that figure. This is strictly 
true so far as relates to equal lead and cut-off, but there 
is still a difference in the effect of the two positions. 
By suitably locating the fulcrum the compression and 
exhaust can be equalized for the two ends of the cylin- 



58 



SLIDE VALVE GEARS. 



der — exactly if the valve have no inside lap, and ap 
proximately if it have such lap. This has not the 
unique interest which belongs to the equalization of lead 
and cut-off, since it can be accomplished by other 
means; but it forms an interesting study, nevertheless. 
The method of accomplishing this equalization is 
shown in Fig. 33, which follows the construction of Fig. 



/ 
/ 
/ 


/ ^ 
/ /^ 

— rt"*M 


r 


ir^h 


Fig. 33 \J /*— 


X j J til T 

1 /& 




<T~ 


<I 



31 up to and including the finding of k, /, but with lead 
zero. Suppose, in the first instance, that the valve has 
no inside lap, and by the methods already described 
find the points of the piston stroke m, n, where release 
and compression should occur, and by arcs whose com- 
mon radius is equal to the length of the connecting rod 
find the corresponding crank positions .y,/. Layoff 
Acs from a giving q, and Bdp from b' giving r. Draw qg 
and rg giving t and u, where the eccentric must be for 
the two equalized compressions. With radius equal to 
the eccentric rod, and centres t, u, strike arcs meeting in 



SETTING THE SLIDE VALVE. $9 

v. Now locate the rock shaft fulcrum at o, such that 
the eccentric rod pin shall pass through k, /, and v, and 
the result will be a valve motion giving equal lead, cut- 
off, release, and compression. If the valve have inside 
lap, then, instead of one point, v, there will be two, 
just as with outside lap there are two points, k, L In 
that case it will be found impossible to so locate o that 
the eccentric rod pin shall pass exactly through all four 
points. It should be then made to pass through k and 
/, and the difference be divided between the two points 
v. The release and compression will then be as nearly- 
equalized as is possible. 



SETTING THE SLIDE VALVE. 

As the parts of an engine valve motion are assem- 
bled two dimensions are lacking: 1st, the angular loca- 
tion of the eccentric relative to the crank ; and, 2d, the 
length of the valve rod. The eccentric is capable of 
being located in any angular position, and the length of 
the valve rod is usually capable of adjustment by means 
of jamb nuts each side of the valve, or some equiva- 
lent means. The setting of the valve involves locating 
the eccentric and fixing the valve at the proper point 
on the rod. There are two distinct steps to the process : 
I. Locating the engine exactly on the centre ; 

II. Locating the eccentric and valve. 

To locate the engine on the centre, proceed as fol- 
lows : Turn the crank to any convenient distance 
above the centre, Fig. 34. Upon the side or face of the 
crank disc or fly-wheel, as most convenient, scribe an 
arc a by means of a tram b swinging from any conven- 



6o 



SLIDE VALVE GEARS. 



rrriir 




SETTING THE SLIDE VALVE. 6l 

ient fixed point on the engine frame or floor. Also 
scribe a line c on cross-head and guides. Turn the crank 
below the centre as shown by Fig. 35, the cross-head 
line receding from its mate on the guide and approach- 
ing it again. When these lines are exactly fair, stop 
the motion and scribe a second line d on the wheel, line 
a, now occupying the position shown in Fig. 35. With 
the dividers find point e, dividing the arc ad in halves. 
When point e is brought fair with the point of the tram, 
Fig. 36, it is clear that the engine will be on the centre. 
Repeat this construction for the other centre. One pre^ 
caution is necessary in relation to the above, in order to 
obviate any error that might arise from looseness in the 
crank pin and cross-head pin bearings : In scribing the 
lines a and d have the crank pin pressing against the 
same brass for both lines. It matters not which brass 
be used, but the same one must be used for both lines. 
To locate the eccentric and valve proceed as follows : 
Locate the eccentric by the eye as near as may be, 
and ahead of its correct position rather than behind it. 
Bring the engine to either centre, as found above, turn- 
ing it in doing so in the directio?i of the proposed rotation 
in order to neutralize any looseness in the connections. 
With the engine on the centre, locate the valve to give 
the required lead, after which turn the engine in the 
direction of its future rotation to the opposite centre. If 
the eccentric is ahead of its correct position, the lead 
for this position will be greater than the first ; if the 
eccentric is behind, the second lead will be less than 
the firsthand probably negative. In either case the 
valve is to be adjusted on the rod to divide the differ- 
ences in the lead. This being done, the valve is cor- 



62 



SLIDE VALVE GEARS. 










SETTING THE SLIDE VALVE. 63 

rectly located on the rod, the lead is equal at the two 
ends of the cylinder, but is too large or too small at 
both. To correct this it only remains to adjust the 
eccentric, moving it in the direction of the rotation until 
the valve have the proper lead. Verify the results, 
and the work is done. 



Part II. 

THE SLIDE VALVE WITH SHIFTING 
AND SWINGING ECCENTRIC. 



The Sude Valve with Shifting and 
Swinging Eccentric. 



THE SLIDE VALVE AT SHORT CUT-OFF. 

The difficulties which impede the use of the plain 
slide valve at short cut-off have been explained at 
length in Part I. Before explaining the shifting eccen- 
tric automatic valve gear, it is necessary to show how 
these difficulties have been surmounted. By referring 
to the section on the Limitations of the Plain Slide 
Valve those difficulties will be seen to be — 

I. Premature release and compression — either of 
which, however, can be made later at the expense of 
making the other earlier still. 

II. Inadequate port opening to steam or, in lieu of 
that, excessive size and travel of valve. 

The first difficulty has been met by increasing the 
speed of the engine. All of the engines employing 
this description of valve gear are of the "high speed" 
type. In such engines a heavy cushion is appropriate 
and necessary to bring the reciprocating parts quietly 
to rest at the centres, and hence the early compression 
ceases to be a radical objection. Indeed, inside lap is 

67 



68 SLIDE VALVE GEARS. 

given to the valve in order to delay the release — there- 
by, as has been explained, still further increasing the 
compression. 

The second difficulty is met by two expedients, the 
first being sometimes employed alone, but more often 
in connection with the second. These expedients are, 
1st, the use of balanced valves, usually of the true pis- 
ton type or of the " pressure plate" type, both being 
perfectly balanced against the steam pressure ; 2d, the 
use of valves having multiple ports, by which the neces- 
sary throw of eccentric is halved or even quartered. 
The use of balanced valves permits the use of valves of 
large size and great throw ; and the use of multiple 
ports gives sufficiently large openings with such throws 
as it is practicable to use. 

It is believed that the first engine to embody the 
above features in connection with a shifting eccentric 
and a shaft governor was the Straight Line ; and hence 
that engine is entitled to be recognized as the progeni- 
tor of a large and vigorous family. So far as known, 
these features were first combined in an engine designed 
by Professor John E. Sweet, built at the Cornell Uni- 
versity shops, and exhibited at the Centennial Exhibi- 
tion. 

That the difficulty of restricted port opening is a real 
one, maybe gathered from any indicator diagram from 
a locomotive with plain valve at good speed and well 
"notched up." Such diagrams invariably show a 
marked fall in the steam pressure on entering the cyl- 
inder ; and it is largely on this account that such per- 
sistent attempts have been made to improve the loco- 
motive valve motion. An appropriate introduction to 



THE SLIDE VALVE AT SHORT CUT-OFF. 



69 



the study of multiple ported valves is found in one not 
necessarily balanced, which was designed more especial- 
ly for use on locomotives, — to which it has been large- 
ly applied, — namely, the Allen valve, shown in Fig. 37. 
In -this valve the seat is shortened and a supplement- 
ary port aa is cast through the valve. This port regis- 
ters with the end of the seat as shown in the figure, 
which represents the valve open by the amount of its 
lead. The course of the steam is shown by the arrows, 
from which it will be seen that the opening at b is added 




Fig, 37 

The Allen Valve. 

to the usual one at c ; and that up to the point where 
the opening at c is equal to the width of passage a, 
the total opening is just twice what it would be with 
the usual form of valve. 

The " pressure plate" type of valve is well shown in 
Fig. 38, which represents the valve of the Straight Line 
engine. The pressure plate AA receives the pressure 
of steam upon its back. It is prevented from pressing 
the valve proper to its seat by means of distance pieces 
above and below the valve, and slightly thicker than the 
valve. Recesses in the plate form in it an exact coun- 



SLIDE VALVE GEARS. 



terpart to the valve seat. The valve slides between 
the seat and plate like a square piston relieved of ail 
pressure. This valve, like those that follow, is shown 




Fig. 38 

The Straight Line Valve. 

open to its lead : and the manner in which the recesses 

in the plate and the passages aa through the valve 

combine to give a double port opening will be seen 

E55 




Fig. 39 

The Woodbury Valve. 

from the arrows. The ledges bb are for the purpose of 
protecting the finished surfaces of the pressure plate 
from the cutting action of the exhaust steam. Some 
designers of double ported valves have thought it best 
to provide double ports for the exhaust, while others 



THE SLIDE VALVE AT SHORT CUT-OFF. 7 l 

have not. The illustrations of both the Allen and 
Straight Line valves will show that the opening to ex- 
haust is amply large without double ports ; but such 
ports increase the quickness of opening to exhaust, and 
so secure a desirable advantage. The valve under dis- 
cussion is provided with them at c, c. Their action is 




Fig. 40 



precisely the same as that of the steam passages a, a, and 
need not be explained further. 

Fig. 39 shows the valve of the Woodbury Engine Com- 
pany. It combines the method of action of the Allen and 
Straight Line valves, and so secures four port openings 
to steam and two to exhaust. Openings a, b act pre- 
cisely like those of the Straight Line valve, and open- 
ings c, a act substantially like the supplementary port of 
the Allen valve. This will be seen more clearly by re- 



72 



SLIDE VALVE GEARS. 



f erring to Fig. 40, which represents a plan of the Wood- 
bury valve. Passages ^,/are cast through the valve to 
act in conjunction with the openings c, d of Fig. 39, in 
the same manner that the passage aa of Fig. 37 oper- 
ates in conjunction with opening b of the same figure. 
Ledge g acts to protect the finished surfaces of the 
cover plate from the action of the exhaust in the same 
manner as ledges b, b of the Straight Line valve. 

Fig. 41 illustrates the valve of the Armstrong engine, 




Fig. 41 

The Armstrong Valve. 

in which the action of the steam and exhaust edges of 
the valve is reversed from the usual practice. The 
steam enters at a, and the outer edges of the valve con- 
trol the exhaust. The steam pressure tends to lift the 
cover plate, and it is therefore held down to its seat by 
means of the bridle b. The action of the steam ports 
will be seen from the arrows. This valve gives four 
openings to steam and two to exhaust. 

The Rice valve (Fig. 42), like the last example, takes 



THE SLIDE VALVE AT SHORT CUT-OFF. 



71 



steam from the inside. It gives two openings to steam 
and two to exhaust. The relief plate aa is in this in- 
stance a piston fitting the cylinder bb, this cylinder be- 




Fig. 42 

The Rice Valve. 

ing bolted to the floor of the steam chest. The pres- 
sure of steam within this cylinder forces the piston 
toward the valve, which, however, it is prevented from 




Fig. 43 

The Arraington and Sims Valve. 

touching by means of distance pieces slightly thicker 
than the valve, and similar to those already described 
in connection with the Straight Line valve. 



74 



SLIDE VALVE GEARS. 



Fig. 43 illustrates the Armington and Sims valve, 
which is a true piston valve with double ports. The 
course of the steam' is shown as heretofore by the 
arrows. 

Fig. 44 shows the Ide double ported valve, which, 
like the last, is a piston valve. 




Fig. 44 

The Ide Valve. 

Of an entirely different type is the Giddings valve as 
used in the Russell & Company engine. This valve is 
shown in Fig. 45. Steam enters at a and exhausts at bb. 
Each end of the valve acts in much the same manner 
as the Allen valve, as will be understood from the arrows, 
while over all is cast a case c. The steam entering from 
the inside of the valve, its pressure would, if not coun- 
teracted, lift the valve from its seat. This is prevented 
by the use of "needle ports" (not shown), one connecting 
the live steam space within the valve to the body of 
the valve chest, and the second connecting the chest to 
the exhaust. The action of these ports is explained by 
Mr. Giddings as follows: " The steam is taken under 
the valve, which would result in throwing the valve off 



THE SLIDE VALVE AT SHORT CUT-OFF. 



75 



the seat. This must be counteracted by pressure on 
the back of the valve sufficient to overcome the ten- 
dency to leave the seat. This I obtain by the small 
needle port communicating with the live steam passage 
on the inside of the valve. If there were no outlet 
this would soon result in an excess of pressure nearly 
equivalent to steam pipe pressure on the back of the 
valve, which would produce a hard working -valve. To 
avoid this, I put another needle port opening, commu- 
nicating with one of the exhaust ' D's ' of the valve. 




Fig. 45 

The Giddings Valve. 

The resulting pressure due to these two openings is 
just sufficient to overcome the tendency to leave the 
seat." 

A remarkable feature of this valve, not attained by 
any other so far as known to the author, is the use 
made of the supplementary passage d. After the com- 
pression has commenced, and before opening to admit 
live steam from the steam supply, this passage opens 
into communication with the regular steam port. This 
increases the volume into which the steam is compressed, 
without, however, increasing the clearance space from 
which the steam is exhausted, since this supplementary 



7 6 



SLIDE VALVE GEARS. 



port is never in communication with the exhaust. This 
is described by Mr. Giddings as follows : 

" We find by increasing the capacity of the carry over 
port or portchamber, that we can use it as a reservoir 
or port into which to pack the surplus compression of 
a single valve automatic movement, thereby giving us 
a peculiar offset in the compression curve, and giving 
us from io to 12 per cent increase of area, and a con- 
sequent increase of power from a given sized engine. 
The amount of this is entirely within our control by a 




Fig. 46 



variation of the cubical capacity of this passage way, 
thereby enabling us to get the compression curve down 
in the corner, something after the manner of the four 
valve engine cards." 

This feature is of such unique interest that indicator- 
cards from one of these engines (Fig. 46) are introduced 
to illustrate it. The offset mentioned will be seen at 
aa, the dotted line b representing the compression 
curve that would have resulted but for this provision. 

The shifting eccentric valve gear, in connection with 
which all these valves are used, requires that the valve 



EQUAL LEAD AND CONSTANT LEAD. 77 

shall have an excess of port opening and travel at the 
late cut-offs in order that they may be sufficient at the 
early cut-offs. Inspection of any of the valves illustrated 
will show that with large travels the supplementary port 
becomes closed after the main port is well opened ; and 
with such travels the effect of the supplementary port is 
merely to increase the quickness of port opening and 
closing. 

* EQUAL LEAD AND CONSTANT LEAD. 

The lead of a valve may vary in two ways, and to 
prevent ambiguity it is necessary to define and follow 
an exact use of terms. The reader is asked to note 
carefully the following explanations of the terms equal 
lead and constant lead. They will be used hereafter 
strictly as defined, and it is necessary that they be 
clearly understood. 

Equal lead implies that the lead is alike at the two 
ends of the cylinder. Constant lead implies that the 
lead does not change for different grades of expansion. 
An engine might have equal lead for one grade of ex- 
pansion and unequal lead for another grade, or the 
lead might be equal at all grades without being con- 
stant ; that is, the lead at the two. ends of the cylin- 
der might be always alike, but larger at both ends for 
three quarters cut-off than for one quarter. So, also, 
an engine might have constant lead without equal lead ; 
that is, the lead might not change for different grades 
of expansion, but at the same time be always larger 
for one end of the cylinder than for the other. 

The above distinctions are radical and important, 



78 SLIDE VALVE GEARS. 

and it is necessary that they be clearly seen in order to 
understand what follows. 



THE SHIFTING ECCENTRIC, f 

The expedients which are employed for making what 
is geometrically the plain slide valve available for early 
cut-offs having been explained, it remains to describe 
how the same valve can be made available for different 
cut-offs. 

In Fig. 47 let the circle abc represent the eccentric 
path of a given eccentric in the Bilgram diagram, the 
eccentric centre being at d, and L and / being, as usual, 
the steam and exhaust lap circles. Let the centre of 
the eccentric be shifted from d to d', dd' being a 
straight line perpendicular to ac. There will thus be 
formed a new eccentric path a'b'c' . Laying off b'd' up- 
ward from c', will locate Q ', the new centre of the lap 
circles. From this centre the lap circles maybe drawn 
in the usual way, and from them the crank positions A 
for the new point of cut-off, B for exhaust closure, and 
C for release may be found. Since bd equals cQ, and 
b'd' equals c'Q', and since dd' is perpendicular to ac, it 
follows that QQ ' is parallel to ac : hence the lead open- 
ing has not been changed. The lead angle, however, 
has clearly been increased, and the port opening has 
been reduced. In the same way, the eccentric may be 
shifted still further on the line dd', and new points of 
cut-off, release, and compression, and new values of the 

f Throughout this and the following section the angularity of the 
connecting and eccentric rods is neglected. 



THE SHIFTING ECCENTRIC. 



79 



port opening, found. Finally, if the eccentric be shifted 
to the position d° on the line ac, the point Q will be lo- 
cated at Q°, when the port opening will be reduced to 
the lead opening and the cut-off will take place as much 
after the centre as the lead did before it. In all posi- 

A 




Fig. 47 

tions the lead opening will be constant. If the valve 
have multiple ports, when the travel becomes so reduced 
as to bring them into action, the result will be to give 
double or quadruple the opening shown by the diagram, 
as the case may be. Should the movement of the ec- 
centric be continued below the line ac, the result would 



80 SLIDE VALVE GEARS. 

be to reverse the direction of the rotation. The study 
of reversing engines is, however, beyond the scope of 
the present work. 

An eccentric arranged for adjustment on straight 
line dd°, as in this illustration, is called by the author a 
shifting eccentric* 

So far as known to the writer, there are but two en- 
gines in the American market which employ a shifting- 
eccentric. These are the Armington and Sims and the 
Russell (Giddings) engines. The former obtains prac- 
tically a straight line motion of the eccentric centre by 
means of a combination of two eccentrics, while in the 
Russell engine the required motion is obtained by means 
of a straight guide keyed to the shaft and appropriate 
wings attached to the eccentric. 

THE SWINGING ECCENTRIC. 

Instead of shifting the eccentric across the shaft in a 
straight line as in the last examples, most designers have 
preferred to swing it by an arm cast in one with itself, 
and pivoted to an arm in the fly-wheel or other con- 
venient piece. Such an eccentric is called by the author 
a swinging eccentric, and its effect upon the steam dis- 
tribution, as distinguished from the shifting eccentric, 
is to vary the lead opening at different points of cut-off. 
The nature and degree of this variability depends in 
large degree upon the location of the pin from which 

* For want of another word, the term shifting eccentric is also used 
as a general expression which includes both shifting and swinging 
eccentrics. This double use of the word will not, however, cause con- 
fusion. 



THE SWINGING ECCENTRIC. 



8l 



the eccentric is swung. If the pin is on the same side 
of the shaft as the crank, and in the centre line of the 
crank, as in Fig. 48, the path of the eccentric across the 
shaft is the arc dd°. The path of the point Q will then 
be a similar arc QQ°, with the same radius and with its 
centre located in the line ef. It is clear from the posi- 
tions of the various lap circles that the lead opening 




will not be constant with this arrangement, but will be 
greater in the early cut-offs than in the late ones. The 
action upon the other events of the stroke is substan- 
tially the same as that of the shifting eccentric. With 
the pin located in the centre line on the opposite side 
of the shaft from the crank, as in Fig. 49, the arc in 
which the eccentric swings has its convexity reversed 



32 



SLIDE VALVE GEARS. 



from the last figure. The path of the point Q will also 
be reversed, and instead of receding from the centre- 
line in the early cut-offs, it will approach it, thus dimin- 
ishing the lead opening in those cut-offs. This diminu- 
tion of lead may be carried so far as to make the lead 
zero or even negative in the early cut-offs — a fact which 




Fig. 49 



will be shown on the diagram by the earlier steam lap 
circles crossing the horizontal centre line. The same 
result of a decreasing lead in the early cut-offs can be 
obtained with the eccentric swing pin on the same side 
of the shaft as the crank, but raised above the centre 
line as in Fig. 50, in which the swing pin is located on 
the line dg extended. Similarly, by raising this pin 
when located opposite to the crank, an increasing lead 
can be obtained. By locating the pin half way between 



THE SWINGING ECCENTRIC. 



83 




Fig. 50 



— I— 



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rfi I 1 


1 i 


■77 


\ \ 


'■ / 


\ \ 


/ / 


\ \ 


/ / 


\ \ 


/ / 


\ \ 


/ / 


\ V 


/ / 


\ V^ 


/ / 






V» 


^ 






% 


51 



8 4 



SLIDE VALVE GEARS. 



the positions of Figs. 48 and 50, on the line hi of Fig. 
51 the lead will be the same at the smallest as at the 
greatest throw ; and by suitably placing it as in Fig. 52, 
the lead can be made alike for any two expansions de- 
sired. In this construction the two points of cut-off 



^~^\ 


-— - y| / 






y \ / 


^dpy^\ 


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\w ^ \ 


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— -^ jzl/P \ \ 


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' ' ' 


1 \ 




\ \ 




y 

/ 
/ 


\ 


/ 


\ 


s 


\ 


y 


\ 


^ 


•>». 


*^ 







Fig. 52 

for which equal lead is desired are decided upon, and 
the corresponding crank positions A, Bare drawn. The 
lap circles are drawn in the usual way for A and B, 
the lead being made the same for both. Points Q and 
Q' are then transferred to d and d', and the eccentric is 
so hung that its centre shall pass through the points 
d and d' . 



THE ANGULARITY OF THE ECCENTRIC ROD. 85 

As has been pointed out, if the valve have a negative 
lead in the early cut-offs, it will be shown in the diagram 
by the lap circle going below the horizontal centre- 
line. In this case if the cut-off be made early enough 
the lap circle will pass through the centre of the shaft. 
This marks the point where the port opening becomes 
zero by reason of the eccentric throw becoming re- 
duced to equality with the lap. For any smaller throw 
there is no admission whatever. 

Designers have usually endeavored to obtain as nearly 
a constant lead as possible. The author considers, how- 
ever, that for stationary engines, where £he speed is 
fixed, a lead decreasing in the early cut-offs is more 
suitable. That the lead should be equal at the two 
ends of the cylinder, there is, however, no question. 
This entire subject will be discussed at greater length 
in the section on Equalized Lead. 



*THE ANGULARITY OF THE ECCENTRIC ROD. 

Thus far in Part II the influence of the angular vi- 
bration of both connecting and eccentric rods has been 
ignored. It will be understood that primarily both 
connecting and eccentric rods produce the same distor- 
tions with the shifting as with the fixed eccentric. 
There is, however, with the shifting or swinging eccen- 
tric an additional distortion produced by the angularity 
of the eccentric rod growing out of the fact that the 
vibration of that rod varies in amount with the varying 
throw of the eccentric— the small throw due to an early 
cut-off giving a small angular vibration, and the large 
throw due to a late cut-off giving a larger vibration. 



86 



SLIDE VALVE GEARS. 



Taking up first the case of the shifting eccentric in 
Fig. 53," let A, B represent the crank pin of a shifting 
eccentric engine when on the dead centres, a, b being 
the corresponding positions of the eccentric centre at its 
greatest throw, h, i at its mean throw, and ^,/at its 
smallest throw. The positions of the eccentric rod for 
mean throw of the eccentric are shown at ch, di, and 
the valve in both positions is open by the amount of 
its lead, as shown by the upper valve sketch for c, and 
the lower one for d. Let the path of the eccentric 




jP 






a 




£— -r*- — 


r~? 




A 


B 

Q 


Q 


\\i 


a f 




Fig. 53 


V^ 









centre, when shifted across the shaft to change the ex- 
pansion, be a straight line occupying the position ae 
for. crank position A, and bf for crank position B. Im- 
agine the crank on the centre A, and shift the eccen- 
tric toward e. Obviously point c will be moved to the 
left, and the lead will be disturbed. For crank posi- 
tion B the same is true ; and what is still worse, while 
the movement for crank position A decreases the lead, 
that for B increases it. If, with crank at A, the eccen- 
tric be shifted towards a, and with crank at B towards 

* See foot-note, page 55. 

This feature of the present diagrams shows a greater irregularity in 
the lead in the usual form of construction, as well as in the form to be 
described, than actually obtains with working proportions. This, how- 
ever, for the present purpose, is rather an advantage than otherwise. 



THE ANGULARITY OF THE ECCENTRIC ROD. 87 

b y the lead at the two points will be disturbed in the op- 
posite directions; i.e., for position^ the lead will be in- 
creased, and for B decreased. The broad fact is evi- 
dent, that, owing to the varying angularity of the ec- 
centric rod, an engine laid out as shown in Fig. 53 could 
not have a constant lead, and it could only have an 
equal lead for some one (selected) grade of expansion. 
With a swinging eccentric, the simplest case is where 
the eccentric swings about a point which, with crank 
at A, Fig. 54, coincides with c. Thus, suppose a 




large disc keyed to the shaft, and arrange the ec- 
centric to swing about a pin fixed to the disc, the 
centre of the pin for crank position A coinciding 
with c, Fig. 54. Now shift the eccentric from h to- 
wards e or a, and c will not be disturbed. When, 
however, the crank is at B } the pin c will be at g ; and 
if the eccentric be shifted from i towards /or d, point d 
will obviously be disturbed more than in the corre- 
sponding movement of Fig. 53; and it may be said in 
general, that with the eccentric rod arranged in the 
common way, as shown in Fig. 53, any change in the 
path of the eccentric across the shaft, to correct the in- 
constant lead at one dead centre, will only make mat- 
ters worse at the other, and by no possible modifica- 



88 



SLIDE VALVE GEARS. 



tion can the lead be made equal for more than one 
grade of expansion. 

The arrangement of Fig. 54, however, while of inter- 
est and value in a theoretical study of the subject, is of 
no practical importance, because its use would require 
so large a disc for the attachment of the eccentric 
swing pin as to be impracticable. It therefore be- 
comes necessary to examine the situation with the ec- 
centric swung from a position nearer the shaft. Let 
the pin be located at the centre of the crank pin — a 
common position — as in Fig. 55, the eccentric rod 
being much longer than the crank, as it always is in 
practice. In that case the actual path of the eccentric 




for crank at A will be to the right of ae of Fig. 54, and 
to the left of bf\ consequently the lead will increase 
at both ends of the cylinder for short cut-offs, but the 
increase will plainly be greater for crank position B 
than for A. The result is a lead increasing in the early 
cut-offs, but increasing much faster for one end of the 
cylinder than for the other, and hence equal at the two 
ends of the cylinder for one grade of expansion only. 
Similarly it might be shown that by swinging the ec- 
centric from a point diametrically opposite the crank 
pin the lead would decrease in the early cut-offs (see 
Fig. 49), but decrease much more rapidly for one end 






EQUALIZED LEAD. 89 

of the cylinder than for the other ; and it is clear that 
whatever quality is sought for in the lead, and deter- 
mined so far as the Bilgram diagram can do it, it will 
in fact be modified by the angular vibration of the ec- 
centric rod. It seems unnecessary, however, to exam- 
ine the subject in detail further. 

* EQUALIZED LEAD. 

So far as known to the author, the only engine in 
which any attempt is made to correct the distortions 
which have just been explained is the Straight Line. 
The valve motion of this engine, like its mechanical 
details, is an exhibition of refined ingenuity which it 
would be difficult to surpass. In the following it will 
first be explained how the engine was originally built 
to secure a substantially constant lead, and after that 
the present construction will be shown. The con- 
struction to be described is essentially the same as that 
already used in equalizing the cut-off of fixed-eccentric 
engines (page 54), and it should be understood that 
the present use of that construction was the original 
one — its use for equalizing the cut-off being in fact 
an offshoot of its original use for equalizing the lead. 
In equalizing the lead as well as the cut-off, two 
types of rocker are possible. The first type of rocker 
is shown in Fig. 56, the parts being lettered as in 
the three preceding figures. From h and i, he and id 
are drawn parallel to the centre line, and each is 
made equal to the length of the eccentric rod. The 
rocker fulcrum is then so located at that the pin 
for the eccentric-rod shall describe an arc passing 



90 



SLIDE VALVE GEARS. 



through c and d. The pin for the valve rod is located 
as usual, m belonging with c, and n with d. The eccen- 
tric is shifted by being swung from a pin, whose loca- 
tion for crank position A coincides with c. As ex- 
plained in connection with Fig. 54, the disturbance of 
the lead for crank position^ is thus eliminated. When 
the crank is at B, c is at g in line with id. In this 
position of the parts, shifting the eccentric on the line 




frfwill disturb the lead a trifle, though much less than 
in the constructions of Fig. 53 or 54. We have here, 
then, a construction which eliminates the disturbance 
for crank position A, and practically eliminates it for B f 
and thus secures substantially a Constant lead. Com- 
paring Figs. 54 and 56, the essential difference in the 
two plans is apparent. In Fig. 56, ch and di are par- 
allel, and hence both c and g are in line with the eccen- 
tric rod position to which each belongs ; whereas in Fig. 
54 ch and di are not parallel, and hence, while c is in line, 
^•is not, and cannot be made so. The construction so 
far explained, would, however, lead to inconvenient 
dimensions of some of the parts. The centre of motion 
for shifting the eccentric is therefore in practice moved 



EQUALIZED LEAD. 



91 



inward from c to some convenient point k on the line 
ch, the eccentric rod pin still remaining at c. The po- 
sition of k for crank at B is of course /. This change 
introduces a trifling error for crank position A, and by 
an equal amount increases the existing error for B; but 
the final irregularity is infinitesimal as compared with 
Fig. 53 or 54, and the mechanism accomplishes its ob- 




Fig. 57 a 



ject — obtaining a practically constant and equal lead 
at all grades of expansion. 

The second type of rocker introduces no material 
change in the lay-out. For an engine with the steam 
chest on top of the cylinder it is illustrated in Fig. 57, 
the parts being lettered to correspond with Fig. 56. 
This type of rocker reverses the motion of the eccen. 
trie, and hence positions a, b, change places as shown. 



9 2 



SLIDE VALVE GEARS. 



As the Straight Line engine is actually built, how- 
ever, the steam chest is on the side of the cylinder, and 
hen^e the second type of rocker takes the unusual 
form of Fig. 58. There is, however, no change in the 
essential principle of the construction, which is, that the 
two positions of the eccentric rods which belong with 
crank positions A, B shall be parallel to one another. 
The object of using this form of rocker is as follows: 




n m 



Fig. 58 



This valve motion, like the usual form, when set for 
equal lead, gives a larger port opening for one end of 
the cylinder than for the other. It is well known that 
the speed of the piston is faster in the end of the cylin- 
der farthest from the crank shaft. Now the second 
type of rocker gives the large port opening to that end 
of the cylinder in which the piston travels the faster, 



EQUALIZED LEAD. 93 

while the first form gives the reverse relation. Hence 
the choice in the construction. 

As now built, however, the Straight Line engine has a 
decreasing lead in the early cut-offs, becoming in fact 
negative in the earliest grades. The reason for this 
change in practice is as follows : In shifting eccentric 
engines, as is well known, the compression increases as 
the cut-off grows shorter. The total cushion by which 
the momentum of the reciprocating parts is arrested 
is the sum of the exhaust cushion and the lead cushion. 
Now if the total cushion is to be constant at all points 
of cut-off, as it should be, the lead must decrease as the 
compression increases, and at the early cut-offs the lead 
should be negative. Furthermore, in such engines, as 
has been explained, both the release and compression 
for early cut-offs occur earlier than is desirable. Now 
by laying out two valves for the same cut-off, one with 
positive and the other with negative lead, it will be 
found that the valve with negative lead gives consid- 
erably later release and compression than does the one 
with positive lead. In other words, the introduction 
of negative lead at the early cut-offs, in addition to off- 
setting in a measure the increasing compression, pro- 
longs the expansion, thereby getting more work out 
of the steam, and also delays the compression, thereby 
still further reducing the cushion. The result is accom- 
plished as shown in Fig. 59, which is a modification of 
Fig. 58. The point k, instead of being on the line di, 
is placed above it. This brings / equally below ck, ex- 
tended ; and, as will be seen by referring to the upper 
valve sketch for m and the lower one for n, reduces 
the lead for both crank positions A and £, as the eccen- 



94 



SLIDE VALVE GEARS. 



trie is shifted inward towards e and /. If the elevation 
of k above di is sufficient, the lead at the early cut-offs 
will obviously be negative. To fully appreciate the 
merit of this construction, Fig. 59 should be compared 
with Fig. 53, when it will be seen that while in Fig. 53 
shifting the eccentric inward from h, i, decreases the 
lead in the upper valve sketch, it increases it in the 
lower one ; in Fig. 59, on the other hand, shifting the 

,d 




el 



eccentric inward from /i, t, decreases the lead in both 
valve sketches. 

Again, Fig. 59 should be compared with Fig. 55, and 
with the suggested companion to it having a decreasing 
lead in the early cut-offs, when it will be seen that 
while the plans are essentially alike in having an incon- 
stant lead, they are unlike in that in Fig. 59 the lead 
is substantially equal at both ends of the cylinder 



EQUALIZED LEAD AND CUT-OFF. 95 

throughout the range, but in Fig. 55 it is equal at one 
grade of expansion only. 

* EQUALIZED LEAD AND CUT-OFF. f 

It has been shown how, by different methods of pro- 
portioning the parts, the same mechanism can be laid 
out at will to give either exact equalization of the cut- 
off in fixed eccentric engines, or approximate equaliza- 
tion of the lead in shifting eccentric engines. It re- 
mains to be shown how a proportion of parts can be 
found which will satisfy both constructions, and thus 
obtain a practically constant and equal lead, an ex- 
actly equal cut-off for any chosen grade of expansion, 
and approximately equal cut-offs for all grades. 

Referring again to Fig. 56, it appears that the funda- 
mental principle of its construction is the diminution 
of the inclination to one another of the lead positions of 
the eccentric rod; and, referring to Fig. 31, it appears 
that the fundamental principle of its construction is 
the direct reverse of this, i.e., the increase of this incli- 
nation. It hence appears at once that the construc- 
tions of Figs. 56 and 31 are incompatible, and cannot 
be reconciled with one another. Comparing Figs. 57 
and 32, on the contrary, it appears that in this general 
way they agree ; but while in Fig. 57 the inclination of 
he and id is reduced to actual zero, i.e., the rods are 
made parallel, in Fig. 32 al and bk are still inclined at 
an appreciable angle. Now the inclination of al and 
bk to one another in Fig. 32 can be varied at will by 

f First published by the author in the American Machinist for 
.March 14, 1889. 



g6 SLIDE VALVE GEARS. 

changing the length of the eccentric rod ; and by- 
choosing a proper length they can be made parallel, 
and the proportions so found will satisfy the construc- 
tion for equal lead, and for the particular grade of ex- 
pansion for which it should be drawn for equal cut-off 
likewise. For other grades it will, of course, satisfy the 
construction for equal cut-off only approximately. One 
qualification must, however, be made. In Fig. 57, A 
and B are located at the dead points, while in Fig. 32 
they are located at the points where admission occurs, 
and these are not usually the dead points. It will 
simplify matters to make these points coincide by con- 
sidering, in the first instance, an engine with a lead of 
zero. In Fig. 60 the construction of Fig. 32 is repeated 
for the mean throw of the eccentric and with lead zero, 
but with several lengths of eccentric-rod, giving a cor- 
responding number of points k' , k" , k" f , /', /", /"'. It is 
plain that the inclination to one another of k'b and 
I' a is less than that of k"b and I" a, which in turn is 
less than k'"b and I'" a, the degree of inclination de- 
pending on the length of rod used. If a length of rod 
can be found such that its two positions shall be paral- 
lel to one another, the rod so found will obviously sat- 
isfy the constructions for both equal lead and equal 
cut-off.. This length is found in the following manner: 
It is obvious that all the points k' , k", etc., are on the 
straight line pg, and similarly /', I", etc., are on qg\ 
therefore, draw pg and qg. Assume a trial length of 
eccentric-rod, and with centres a, b, strike arcs giving 
k, /, such that bk and al are parallel, repeating the 
construction with different lengths of rod until the 
correct length is found. Locate the rocker fulcrum so 



EQUALIZED LEAD AND CUT OFF. 



97 



that the eccentric rod pin shall pass through k and /. 
Now positions a/, bk obviously satisfy the construc- 
tion for equal cut-off, and, being parallel, they also sat- 
isfy that for equal lead ; and an engine with its valve- 
motion laid out in this manner will have approximately 
equal and constant lead, equal cut-off for that eccen- 
tric throw for which the construction is made, and an 




approximately equal cut-off for other positions of the 
eccentric. 

The construction of Figs. 56, 57, and 58 was made 
with the crank on the centre, while that for Figs. 31 
and 32 was made with the crank in position for ad- 
mission of steam, and in Fig. 60 these methods were 
reconciled by supposing the admission to occur on the 
centre. No material error would be introduced if this 



9 8 



SLIDE VALVE GEARS. 



method were followed in all cases ; but if it is desired 
to follow the strictly correct method, it can be done in 
the following manner : Fig. 61 is a reproduction of Fig. 
32, constructed for the mean throw of the eccentric, 
with some additions. Find points b x , a x and k, , l x cor- 




responding with crank positions A', B', and draw k x b l 
and / 1 a l . Now the construction of Fig. 32 gives the 
positions of kb and /«, while it is desired to make £,£, 
and l l a l parallel by suitably selecting the eccentric rod 
length. This should be done by trial, as before, re- 
peating the trial until the desired result is reached. 



PART III, 



THE SLIDE VALVE WITH INDEPENDENT 
CUT-OFF. 



The Slide Valve with Independent 
Cut-off. 



INTRODUCTORY REMARKS. 

An early cut-off being a necessity for an economical 
use of steam, it comes about that with valves of the 
construction previously described the leading consider- 
ations in their design are those pertaining to the steam 
side of the valve. The valve and eccentric being de- 
signed with reference to the steam side, so as to secure 
an early cut-off, there is little that can be done with 
the exhaust side beyond reconciling conflicting require- 
ments as well as possible. In engines provided with 
independent cut-off valves this condition no longer 
holds : the exhaust can usually be arranged to suit the 
designer's fancy; and it hence follows that in such 
engines the leading considerations in the design of the 
main valve are usually those pertaining, to the exhaust. 
It is essential that the exhaust have a certain lead, in 
order that the cylinder may free itself of steam, and, 
on the other hand, this lead should be no greater than 
is necessary for this purpose, since that would involve 
exhausting the steam at a point where it might still do 



102 SLIDE VALVE GEARS. 

some useful work. The determination of the point of 
release is, therefore, a leading factor in the design of this 
class of valves. It is not to be expected that there will 
be any close agreement in a detail of this character in 
the work of different designers; but, as a general rule, 
modified somewhat by questions of piston-speed, etc., 
it may be said that release should occur at from 93 to 
95 per cent of the piston stroke.* The other event of 
the exhaust side of the valve, the compression, is de- 
termined, it must be owned, largely by the taste and 
fancy of the designer. A late compression by requiring 
a small exhaust lap conduces to a small travel of the 
valve, which, if it is to be unbalanced, is a desirable 
feature. The features of the exhaust side of the main 
valve and the port opening to steam having been 
settled, the steam side is determined by the force of 
circumstances. To give the proper points of exhaust 
opening and closure, the steam lap will usually be 
small and the cut-off late. This, however, is of no 
consequence, as the cut-off valve is introduced for the 
express purpose of providing for it. 

THE GONZENBACH VALVE GEAR. 

A description and analysis of this valve gear is here 
given as an introduction to those which follow. It is 
now seldom employed. It comprises two valve chests, 
two valve seats, and two valves, as shown in Fig. 62. 
The lower or " main valve" is driven by a fixed eccen- 

* In engines of slow rotative speed — for example, Corliss engines 
and others of similar general character — the release will frequently b< 
found to be somewhat later than the figure given in the text. 



THE GONZENBACH VALVE GEAR. 



103 



trie, and determines the admission, release, and com- 
pression of steam. The upper or "cut-off valve" is 
used solely for the purpose of the cut-off, and is usu- 
ally of the gridiron type, in order to secure quickness 
of cut-off with moderate travel. It is driven by an 
eccentric of its own, which, if the expansion is to be 
varied, must be turned forward or backward, as the case 




Fig. 62 

The Gonzenbach Valve, 

may be, on the main shaft. This movement affects the 
angular advance only, and, unlike the eccentric move- 
ments of Part II, does not change the travel of the 
valve.* 

The action of this cut-off valve is different from any. 
thing that has thus far been examined. The previous 

* The following applications of the Bilgram diagram to the Gonzen- 
bach, and also to the Buckeye and Bilgram valve gears, are substantially 
the same as those previously published (now largely inaccessible) by 
Mr. Bilgram. 



104 



SLIDE VALVE GEARS. 



valves open and close their ports with the same edge, i.e., 
in opening the port the valve draws to one side, and in 
closing it resumes the previous position. This cut-off 
valve, however, opens and closes the port by the port 
in the valve passing bodily across the port in the seat, 
the opening being done by one edge, and the closing 
by the other. Further, the same ports serve for both 
ends of the cylinder ; the valve ports passing over the 
seat ports in one direction for one end of the cylinder, 
and in the opposite direction for the other end. 

It will be seen from Fig. 62 that the cut-off valve 




/ . 




\ 


JV / 

/ 

_y' 



Fig. 63 



Fig. 64 



has negative lap, since the ports are open when the 
valve stands at its central position. The width of port 
in the valve may equal or exceed the width of port in 
the seat. In the former case, the negative lap is equal 
to the width of port ; in the latter, to the distance a of 
Fig. 63. The location of the eccentrics is shown in Fig. 
64, d being the main and d' the cut-off; S being the ad- 
vance angle of the former, and S' of the latter. The 
centres of the lap circles Q and Q\ Fig. 65, are found in 



THE GONZENBACH VALVE GEAR. 



i05 



the usual way, by laying off the angles S and d' up- 
ward from the horizontal centre line. The effect of 
the three ported valve being equivalent to a valve with 
a single port of three times the width and travel, the 
throw of the cut-off eccentric is in the diagram in- 




1 
1 


>? 


\ 


/ 1 \ 


\ 


/ 


\ 


/ / 


\ 




N al l 




i ~~~i" 




\ \ 




\ \ 




\ \ 



/ / 



/ 



Fig. 65 

creased to three times that shown in Fig. 64, and the 
lap circle is likewise drawn, with a radius three times 
the actual negative lap for each port. Starting at 
crank position A, it is clear that the main valve is 
open by the amount of its lead. The cut-off valve is 
at a distance Q'a from its central position, which being 



i06 SLIDE VALVE GEARS. 

less than the negative lap, the cut-off ports are open, — 
a fact which is also shown by the dotted (negative) lap 
circle going below the horizontal centre line. As the 
crank rises, the port opens more widely, up to position 

B. In the original discussion of the Bilgram diagram 
it appeared that when the crank passed through Q the 
valve stood central upon its seat. In that position the 
ports of the present valve stand wide open, — as is 
apparent from the plan of the valve and the present 
diagram alike. Passing crank position B, the valve 
begins to close the port, not by returning toward its 
former position as with previous valves, but by passing 
on to the other side of its centre line, — as is indicated 
in the present diagram, by the perpendicular from Q 
falling upon the opposite side of the crank. 

The closure is completed and cut-off takes place at 

C, which is indicated in the usual manner. From this 
point expansion goes on in the cylinder and lower chest 
together, until crank position D is reached, where the 
main valve closes its port. As has been stated, the ex- 
pansion is varied by changing the angular advance of 
the cut-off eccentric. If d' of Fig. 64 be increased, Q' 
of Fig. 65 will be lowered toward the centre line and 
the cut-off position C of the crank will be shifted to an 
earlier part of the stroke. This change in the cut-off 
will be accompanied by an earlier and earlier admission 
from the upper to the lower steam chest, as will be 
shown by the large lap circle having a larger and larger 
segment below the horizontal centre line. Crank posi- 
tion D extended backward gives the position at which 
the main valve cuts off the steam on the previous stroke, 
and it is clear that the cut-off eccentric might be ad- 



THE GONZENBACH VALVE GEAR. 107 

vanced so far that the admission from the upper to the 
lower chest would occur before the main valve had 
closed its port in the previous stroke ; i.e., in advanc- 
ing the eccentric to obtain an early cut-off the result 
would be to give a second admission of steam at the 
latter end of the expansion. This feature limits the 
range of variation to the expansion which this gear can 
give. The only way to provide a shorter cut-off is to 
increase the lap of the main valve, since this carries 
crank position D backward, and allows the cut-off lap 
circle to be carried farther back before interfering with 
the main valve. 

The principles of this valve, and of the application 
of the diagram to it, can be fixed in the mind by fol- 
lowing the solution of 

Problem VII. A Gonzenbach valve gear is to be 
constructed with a maximum cut-off of f stroke. The 
greatest port opening to steam of the main valve is to 
be ij". Since there is nothing to prevent liberality in 
this respect, the cut-off ports will number three, each 
one inch wide in valve and seat alike. Required the 
shortest possible cut-off, and the positions of the cut- 
off eccentric for the earliest and latest cut-off. 

In Fig. 66 the centre Q of the main valve lap 
circle is found in the usual manner. Lead position 
A and maximum cut-off position B are then drawn. 
At the latest cut-off the cut-off valve lap circle must 
be tangent to A and B, and its radius being three 
inches (three times the port opening), it is easily drawn, 
giving Q f the position of cut-off eccentric for latest cut- 
off. Extending B downward and finding Q" such as 
to make the cut-off lap circle tangent to B extended, 



o8 



slide Valve gears. 



determines crank position C, the earliest cut-off prac- 
ticable with the dimensions given, and also the range 
of movement Q to Q" of the cut-off eccentric. 

It has been shown that the range of cut-off with this 
gear is somewhat limited. Another defect of the ar- 
rangement is the large volume of the lower chest, which 
increases the clearance space during expansion. The 




Fig. 68 



object of a separate cut-off valve is to introduce early 
cut-off, and it is in these early cut-offs that the effect 
of this increased clearance is greatest, making a serious 
discrepancy between the " real " and " apparent" ex- 
pansion. For these reasons, together with the inac- 
cessibility of the lower valve, the plan has largely fallen 
into disuse. 



THE MEYER VALVE GEAR. 



109 



THE MEYER VALVE GEAR. 

In this gear, which has been very extensively used, 
a separate valve is used for the sole purpose of cutting 
off, as in the last example. The general arrangement 
of the valves is shown in Fig. 67, from which it will be 
seen by reference to the dotted lines that the main valve 
is essentially a plain valve of the usual type, with the 
addition of a bridge at each end to form a port through 




Fig. 67 

The Meyer Valve. 

it, and planed upon its back to form a seat for the cut- 
off valves. These cut-off valves are driven by a sepa- 
rate eccentric, and, as shown, the cut-off valve rod con- 
tains a right and a left hand screw upon which the 
valves are threaded. The valve rod has a hand wheel 
upon it, and its connection with the eccentric rod is 
such as to permit its being rotated at will by means of 
the hand wheel. This rotation increases or decreases 
the distance apart of the valves, and thereby changes 
their lap and the point of cutting off. An index is at- 
tached, which, moving over a graduated scale, shows at 
a glance the position of the valves upon the stem and 



I 

110 SLIDE VALVE GEARS, 

the degree of expansion. Occasionally this rotation of 
the valve rod has been connected to the governor, but 
the extent of the movement required and the friction 
incident to the mechanism are so great as to render 
such a plan a questionable success. Unlike the pre- 
vious gear, the angular location of the cut-off eccentric 
is not a matter requiring exactness. In the older prac- 
tice it was customary to place that eccentric exactly 
opposite the crank, or, since that gave the same motion, 
to connect the valve rod to the cross-head by means of a 
lever. This plan is still followed in marine, hoisting, and 
other engines which are to turn in both directions, since 
the motion of the cut-off valves is then correct for both 
forward and backward rotation. In present practice 
the cut-off eccentric of stationary engines is not usu- 
ally placed so far in advance of the main eccentric. A 
common location is forty five degrees in advance. The 
effect of this is to require a smaller movement for a 
given change of the expansion. To offset this advan- 
tage, it reduces somewhat the width of port opening 
given by the cut-off valve and the speed of cutting off. 
The application of the Bilgram diagram to this gear 
is shown in Fig. 68. The locations of the eccentrics 
are shown at d and d' ', the throw of the latter exceed- 
ing that of the former, as is customary in practice. It 
will be understood at the outset that since the lap of 
the cut-off valve is changed to vary the point of cutting 
off, a number of cut-off lap circles will appear in the 
diagram. Some of these will represent positive and 
some negative lap, and the determination of the proper 
lap for different expansions is one of the leading points 
to be determined from the diagram. Since the seat of 



THE MEYER VALVE GEAR. 



Ill 



the cut-off valves is upon the back of the main valve, it 
is clear that the diagram must show the position of the 
former in relation to the latter. Beginning with crank 




Fig. 68 



position A, it is clear that the main valve is advanced 
to the right of its mid position by the distance Qa, and 
the cut-off valve by the distance Q'a! '. The cut-off valve 



112 SLIDE VALVE GEARS. 

is therefore removed from its mid position a distance 
Q'a" greater than the main valve. If it is desired that 
the cut-off shall take place with the crank at A, there 
must be a lap given to the cut-off valve equal to Q'a" . 
Hence the lap circle I' . Similarly for crank position B 
the main valve is at a distance Qb and the cut-off Q'b' 
from the central position. The displacement of the 
main valve is here the greatest by Q'b", and if the cut-off 
valve had a lap of zero the main valve port would still be 
covered by the distance Q'b". Therefore, if the cut-off 
is to occur at this position of the crank, the cut-off valve 
must have a negative lap equal to Q' f b" . Similarly the 
value of the lap required for any cut-off may be found. 
If the range of cut-off is to be from zero to that given 
by the main valve, the positive lap required for the 
former and the negative lap for the latter is easily found, 
and the sum of the two amounts will give the total move- 
ment of each valve on the stem to accomplish the required 
range. The tangents drawn from point Q to the various 
lap circles, and the perpendiculars dropped to them 
from the point Q', form precisely the same construction 
from gasa centre that the diagram for the plain valve 
did from as a centre, and these lines with the lap 
circles give the relations of the two valves to one an- 
other precisely as though the main were a fixed seat 
for the cut-off valve. As in Fig. 15, the distance Oc 
represented the velocity of a plain valve at the moment 
of cutting off, so in Fig. 68 the distances Qa", Qb" repre- 
sent the velocity of the cut-off valve relative to the main 
valve at the same moment. In the figure it will be seen 
that this velocity is somewhat less than the correspond- 
ing velocity for the maximum cut-off by the main valve, 



THE MEYER VALVE GEAR. 113 

and in fact a somewhat sluggish cut-off is a characteristic 
of this valve gear. The only method of quickening this 
velocity is to increase the distance between Q and Q by 
increasing the throw or angular advance of the cut-off 
eccentric. This, however, increases the diameters of 
the lap circles, and the distances which the valves must 
be moved on the stem, together with the length of steam- 
chest to permit the increased movement. If the full 
range of expansion is not required, the entire move 
ment on the stem is available for the limited range, and 
this can be put to good use by increasing the quickness 
of the cutting off ; but generally in practice it is neces- 
sary to adjust the conflicting requirements to one an- 
other with a view to securing the best compromise 
possible. 

The greatest distance apart of the centres of the main 
and cut-off valves, or in other words the half travel of 
the cut-off relative to the main valve, is the distance 
QQ '. Should the cut-off plates be brought so near 
together that the negative lap equalled this distance 
QQ', the cut-off valve would close the main valve port 
for an instant and immediately reopen it. Should this 
happen before the final cut-off by the main valve, it 
would give a readmission of steam. To determine if 
this is possible, strike the negative lap circle in ques- 
tion with radius QQ' . Draw its tangent c through Q 
and a crank line D parallel to the tangent. This crank 
line D comes well within the main valve lap circle, indi- 
cating that the latest possible cut-off by the cut-off valve 
at which the momentary closure occurs takes place after 
the closure of the port by the main valve. Had the line 
D come tangent to the lap-circle it would have indicat- 



ii4 



SLIDE VALVE GEARS. 



ed that the momentary closure of the main valve port 
would have occurred just at the closure of the port by 
the main valve ; and had it fallen without the lap circle, 
as in Fig. 69, it would have indicated that some of the 
later grades of expansion would have been accompa- 



Q T 



r^9 



/ 
/ 

/ 

/ 
1 
1 




// \/\ y 


/ ^-^ / -T^ 


1 




j 


' 1 


\ 


/ 


\ 


/ 


\ 


/ 


\ 


/ 


\ 
\ 


/ 
/ 
/ 


\ 


/ 


\ 


/ 


\ 


/ 


\ 





Fig. 69 

nied with readmission. This is of but little moment, 
as, unlike the previous gear, it affects the late and not 
the early cut-offs ; but it can be easily avoided. Thus 
in Fig. 69, lines C and D being parallel, QQ', which is 
perpendicular to C, is also perpendicular to D. If the 



THE MEYER VALVE GEAR. 



115 



position of Q be altered to Q" , such that QQ" is per- 
pendicular to E, it is clear that D and E will coincide, 
the limiting condition will have been reached, and if 



B 




/ \° 




L— — 


— -ife' A 




^*^\ 


i\0- / 




** \ 


/I \W / J 




^\ 


'JW^^CJ 


/ \ 


/ \ 


/ ' ^^J^"^\ /\ 


/ > 

/ / 




/ <ks A \ 


/ / 




w // J>K \ \ 


/ / 

/ / 
/ / 

, 1 \ 




i7^\ ^ ?"V 


1 




a' a j | 






/ 


\ \ 




/ / 


\ \ 




/ / 


\ \ 




/ / 


\\ 




// 


\ s 




/ /■ 


\ 


\ 


/ / 


\ 


^^ 


^ / 


N 




_^— -" / 


\ 




y 




^ 


S* 




"»«. 


^ 






_ . — 




^~" 





Fig. 70 

the centre of the cut-off lap circles be located slightly 
to the right of Q ", no possible readmission can occur. 
One point requiring attention remains. It is clear 



Il6 SLIDE VALVE GEARS. 

that were the cut-off plates quite narrow, they might 
when screwed well apart pass entirely over the main 
valve ports and readmit steam by their back edges, and 
the width must plainly be made great enough to pre- 
vent this. In Fig. 70 place the crank at the dead-point 
position A, and determine the lap necessary for cut-off 
at that extreme position. The valves are located at dis- 
tances Qa and Q'a' from their mid positions, and Qa" is 
the radius of the required lap circle. As the crank 
mounts upward Qa lengthens and Qa' shortens, until at 
crank position B parallel to QQ ', Qa and Q'a' are equal. 
Beyond B, Qa exceeds Q'a', until at C, Q'a' vanishes. 
Beyond C, Q'a' falls upon the rear side of the crank, and 
at D, Q'a' becomes Q'a 7 '. At this point the distance 
apart of the centres of the valves is Q'd' plus Q d. In 
other words, that distance has diminished from Q'a" to 
zero, and increased again in the opposite direction to 
Qa plus Q'd'. With the crank at A the edge of the 
cut-off plate just closed the port, and at D it will have 
closed the port by a distance Q'a" plus Q'd' plus Qd\ 
and the width of the plate must equal this distance, 
plus the width of the main valve port, plus an allow- 
ance for tightness — say \" . 

THE BUCKEYE VALVE GEAR. 

This exceedingly ingenious valve gear is in one 
sense a combination of the two preceding. To the 
small clearance and mechanical capabilities of the Meyer 
valve it unites the turning eccentric of the Gonzenbach 
with its convenient attachment to the shaft governor."- 
*The Buckeye was the pioneer shaft-governor engine. 



THE BUCKEYE VALVE GEAR. 



117 



At the same time it is not limited in range as is the 
Gonzenbach, and it has a sharper cut-off than either 
one. Balancing and other features of the valve dis- 
guise its relationships somewhat, but discussion of these 
features is beyond the scope of the present work. The 



L. ' 1 




■•- •: ■"'•'- — " " -' ~— " r' 




Fig. 71 

The Buckeye Valve. 

construction of the valve, so far as its action on the 
ports is concerned, is shown in Fig. 71, from which it 
will be seen that it takes steam from within its box-like 
form, and exhausts by its ends into what with other 
valves is commonly the steam-chest. The cut-off 
valves are similar to those of the Meyer system, ex- 
cept that they are secured immovably upon the rod. 

d' 

1 ■ — 




c b 

Fig. 72 

Fig. 72 is an ideal view of the same valve with a diagram 
of the eccentrics. The position of the crank being 
at A, the main eccentric, by reason of the valve ex- 
hausting by its outside edges, is at d. The main 
eccentric and valve rods are connected to a rocker 



Il8 SLIDE VALVE GEARS. 

pivoted at b. This rocker does not change the motion 
of the main eccentric in transmitting it to the valve. 
The cut-off eccentric and valve rods are also connected 
to a rocker, the former at c and the latter at e. This 
rocker is pivoted at f, which pivot is carried by the 
main rocker. It is clear that the motion which the 
cut off eccentric rod imparts to the lower end of its 
rocker is, if the eccentric be properly set, precisely the 
same as that required for a Gonzenbach cut-off valve, 
having its seat in line with the eccentric rod. But the 
distance be always equals eg, or, in other words, the 
motion of the upper end of the cut-off rocker relative 
to the main rocker is the same as that of the lower end 
relative to a fixed valve seat. That is, the motion of 
the cut-off valve relative to the main valve is the same 
as that of the Gonzenbach cut-off valve relative to its 
fixed seat. With the Gonzenbach gear a single set of 
ports through the cut-off valve-seat served for both ends 
of the cylinder, and it was shown that, in consequence, 
there was danger in the early grades of expansion of a 
readmission of steam before final closure of the port by 
the main valve. With the construction of the present 
gear this is avoided, and, properly proportioned, there 
can be no readmission in either the early or late grades. 
The exhaust taking place at the ends of the main valve 
locates the eccentric diametrically opposite from its 
usual position, and the cut-off rocker does the same for 
the cut-off eccentric. The angular position of the cut- 
off eccentric rod also moves the cut-off eccentric from 
the positions shown in Fig. 73 by the same angle. 
Since the action of the cut-off valve is essentially the 
same as in the Gonzenbach gear, it may be represented 



THE BUCKEYE VALVE GEAR. 



II 9 



by essentially the same diagram as in Fig. 73. Q is as 
usual the centre of the main valve lap circles and Q', 
Q", Q'" of the cut-off (negative) lap circle for different 
points of cut-off, Q' being the position for cut-off at 




Fig. 73 

zero, Q" for latest cut-off, i.e., at the main valve closure, 
and Q" for any desired crank position A, The open- 
ing of the ports by the cut-off valves is in this instance 
of little moment, since it occurs during the previous 
stroke, when the admission port for the end of the 
cylinder under consideration is out of action. 



120 



SLIDE VALVE GEARS. 



THE STRAIGHT LINE INDEPENDENT CUT-OFF GEAR. 

Fig. 74 is a horizontal section of a steam cylinder 
fitted with the above valves, the bottom of the figure 







showing the steam and the top the exhaust valve. The 
two are of similar construction, both being fitted with 



STRAIGHT LINE INDEPENDENT CUT-OFF GEAR. 121 



relief plates and multiple ports, and both acting by 
their outside edges. They differ chiefly in that the 
exhaust valve is driven by a fixed, and the steam valve 
by a swinging eccentric. The Bilgram diagram as ap- 
plied to the gear consists of the diagram already 

A B 




Fig.\75 



familiar for the swinging eccentric gear, but with the 
exhaust lap circle occupying a fixed position instead of 
the moving one of the usual swinging eccentric gear. 
Contrary to all previous practice with independent 
valves, this engine is arranged for positive lead in the 



122 SLIDE VALVE GEARS. 

late and negative in the early cut-offs. The object of 
this is as follows : It is generally understood that com- 
pression does not begin to bring the piston to rest until 
the pressure on the compression side exceeds that on 
the expansion side of the piston. With an early cut- 
off this state of affairs occurs at some distance from the 
end of the stroke, but at later cut-off the expansion 
curve is higher and the compression curve does not 
rise so soon to equal it. Hence the effect of the com- 
pression in bringing the parts to rest is lessened at late 
cut-off, and to make up for the deficiency a prominent 
lead is given. 

The application of the Bilgram diagram is shown in 
Fig. 75, in which Q is the centre of the steam valve lap 
circle for greatest throw, cut-off at B ; Q is the fixed 
centre of the exhaust lap circle, and Q" the centre of 
the steam circle with the eccentric shifted for cut-off at 
A, the path of the eccentric centre being QQ' '. It will 
be observed that for cut-off at B the lead is positive 
and at A negative. The fixed position for compression 
is C, and for release D. 

THE BILGRAM VALVE GEAR. 

This gear has been designed to provide a more rapid 
cutting off than the Gonzenbach or Meyer gear. The 
following description is from Mr. Bilgram's book on 
this subject (now out of print): 

Both valves are operated by one single eccentric /, 
Fig. 76 ; the main valve directly by the eccentric rod, 
and the cut-off valve through a peculiar mechanism, 
consisting of four members ; viz. : the link, the rocker, 



THE BILGRAM VALVE GEAR. 



123 




\ 



W 



1 




Fig., 76 



124 SLIDE VALVE GEARS. 

the cut-off rod, and the adjustment lever. The link 
AB being jointed by the pin A to the eccentric rod, 
imparts to the rocker a rocking motion on its fulcrum 
F. The rocker is of a peculiar shape, as shown de- 
tached in the cut, but it virtually represents a bell crank 
(or angular lever) having an angle BFC of about 50 , 
the arm CF of which is about twice as long as the arm 
BF. To the extreme end C of this rocker is jointed 
the cut-off rod, by which the cut-off valve is moved. 
For the purpose of changing the degree of expansion 
the fulcrum F of the rocker can be moved in a circular 
arc, being attached to the end of the adjustment lever 
GF, whose fulcrum G is a fixed point. 

The study of this gear will consist in the investiga- 
tion of the movement of the cut-off valve for several 
positions of the adjustment lever. In every case we 
shall proceed from the neutral position of the rocker 
(found by transferring the eccentric rod to the centre 
of the crank shaft), remembering that the movement of 
the mechanism will be symmetrical to both sides of this 
position. Besides, we shall as usual neglect all com- 
plicating influences resulting from the angularity of 
the several members ; and besides, we shall assume the 
movement of the pin A to be strictly circular and co- 
incident with the movement of the eccentric /. 

At first we move the adjustment lever until the line 
CF of the rocker assumes a vertical position (see Fig. 
jj), the theory for this position being the least compli- 
cated. When the mechanism is in operation, the pin 
A will move in a circle, and hence the points B and C 
will move in the arcs b'b" and c'c" . For the latter arc 
we shall substitute the chord to simplify the theory. 



THE BILGRAM VALVE GEAR. 



125 



When the crank is on its centre, the pin A will occupy 
the position A° corresponding to the position of the 
eccentric /, and since the link AB represents, as it 
were, the eccentric rod for the cut-off gear, we can 
measure the angle of advance 6° = YAA° by drawing 
AY at right angles to BA. The angle CFB being 50 



.-^— -v 



Y\ / / • \ 

<~~~1 "A A ,- / / A 7" ¥--Tf 

j a— --^^ gij U i w/Jtr'T 







-^ 



Fig. 77 

and ^4i? being at right angles with FB, or approximately 
so, it is evident that the angle YAA° = d° exceeds 
the angle of advance of the eccentric / by 50 . Owing 
to the dimensions of the rocker, the travel of the point 
C y and consequently also the travel of the cut-off valve, 
equals double the travel of the main valve ; and hence 
we can rind the ideal eccentric i° of the movement of 
the cut-off valve for the considered grade by advancing 
the line 01 through an angle of 50 and doubling its 
length. 



126 SLIDE VALVE GEARS. 

Next we move the fulcrum F towards the right to 
F' to change the grade, and denote the angular change 
of the rocker by the Greek letter /?. The correspond- 
ing angular change of the link AB is practically the 
same, and the angular advance is consequently farther 
increased by this angle. We can therefore draw the 
line Oi ', but we have yet to find its length. The move- 
ment d'd" of the pin C of the rocker is doubtless the 
same as it was before ; but being inclined, it is only its 
horizontal component d'd° that is transmitted to the 
valve, and the throw Oi' of the ideal eccentric for this 
grade will be less than Oi °. The necessary reduction 
can be made by drawing the line i°i' at right angles to 
Oi', which will be understood when we consider the 
similarity of the triangles Oi'i° and d'd°d" . 

In moving the fulcrum F of the rocker in the oppo- 
site direction we would have found the ideal eccentric 
i", and other positions of the fulcrum F would furnish 
more points of the locus of ideal eccentrics. The angle 
i°i'0 being a right one, it will easily be understood that 
all the ideal eccentrics will be located in a circle of 
which the line Oi° is a diameter. 

These results relate to the absolute movement of the 
valve, and to find the ideal eccentrics for the relative 
movement we move the locus in the direction of and 
through a distance equal to 10. Having thus deter- 
mined the locus j'fj" of the relative movement, we can 
draw the valve diagram, Fig. 78, in the usual manner. 

This diagram now shows that the cut-off can be ad- 
justed to any point between the crank angles OA and 
OE as the angular adjustment of the rocker is not lim- 
ited. It shows, moreover, that this valve gear is distin- 



THE BILGRAM VALVE GEAR. 



127 



guished by the decided rapidity in cutting off. The 
closure of the steam passages is very sharp for all grades 
cuttingoff before the half stroke ; for a later cut-off 
however, this rapidity will get less, until when cutting 
off at OE the rapidity of the cutting off of the cut-off, 
valve will about equal that of the main valve. 




Fig. 78 

The rapidity of the late cut-offs can be improved, if 
desired, by making the arm CFoi the rocker more than 
double the length of the arm BF, whereby the line 0i° 
will be lengthened, and consequently the locus circle will 
be enlarged. This change entails an increase of the ab- 
solute movement of the cut-off valve above twice the 
travel of the main valve. Another measure consists 



128 



SLIDE VALVE GEARS. 



iii increasing the negative lap of the cut-off valve ; but it 
should never exceed the positive outside lap of the main 
valve. A reduction of the angle BFC of the rocker 
would likewise be efficient, but this reduction is at- 
tended by an increase of certain irregularities. 

The sharpness of the cut-off will in reality be slightly 
less than indicated in the diagram, from the fact that 
the movement of the pin A is not circular, as was as- 
sumed, but is more or less flattened. 

The proportioning of the mechanism requires some 







Fig. 79 



care, for on it depends largely the proper operations 
and regularity of the cut-off. To this end we draw the 
rocker BFC (Fig. 79) with the line CF in a vertical 
position and the line BF zX an angle of 50 , and make 
the arm BF from three to four times the throw of the 
eccentric, and the arm CF twice as long. (The figures 



THE BlLCRAM VALVE GEAR. 1%9 

given have been tested by a number of experiments.) 
Then we draw the link AB at right angles to BF and 
make it about f of the length of CF. The eccentric 
rod OP can next be shown in its neutral position, pass- 
ing through the end A of the link. The cut-off rod 
CP° can likewise be shown. 

To find the length and position of the adjustment 
lever GF, it is necessary to make a model of thin wood 
or veneer, consisting of the eccentric rod, the link, the 
rocker, and the cut-off rod. Next we draw the orbit of 
the eccentric, and on it the exact position of the eccen- 
tric, say for every one sixth of the stroke of the piston, 
which may be done in the following way, identifying 
the eccentric path with the path of the crank pin : 

We divide the diameter of the orbit passing through 
the initial position of the eccentric / in six equal parts, 
and draw the projection arcs of the proper radius 
through those points as shown. The next thing to be 
done is to attach the model to the drawing by joining 
the parts properly together with pins or thumb tacks, 
and fastening the ends P and P° of the rods to two 
slides representing the valves. The right end of the 
eccentric rod may be provided with a needle point 
which at 'first we put in the centre 0, when we set the 
rocker directly over the position shown in the drawing, 
and mark the relative position of the two slides repre- 
senting the valves. Then we make two additional 
marks on one of them, at a distance equal to the as- 
sumed negative lap of the cut-off valve, to show the 
relative position for the cutting off on either side. 
Suppose now we desire to find the proper position of 
the rocker for cutting off at the point 1. To this end 



13° SLIDE VALVE GEARS. 

we set the needle point of the eccentric rod in the point 
1 of the fore stroke, and fix the valves for cutting off 
at the proper side, when we will find that the end F of 
the rocker cannot be moved but in a certain curve. 
This curve we mark on the drawing by setting a needle 
point into the rocker and making a slight scratch on 
the paper. Thereupon we attach the eccentric to the 
point V of the return stroke, fix the cut-off valve to the 
point of closure of the other passage of the main valve, 
and mark another curve by the point F of the rocker. 
The juncture F' of the curves must of necessity be the 
exact position of the fulcrum of the rocker when we de- 
sire to cut off at one sixth of the stroke. In this way 
we can find the required position of the fulcrum for all 
the other grades, which will be found to form a curve. 
By substituting a circular arc for this curve, osculat- 
ing as closely as possible, we obtain the location and 
length of the adjustment lever GF. An arc can gener- 
ally be found to agree with the constructed curve with 
an almost absolute precision ; and hence it will be seen 
that this valve gear will admit of a practically perfect 
equalization of the difference between fore and return 
stroke. 



INDEX. 



PAGE 

Admission 13, 19, 21, 23 

Advance angle 18 

Allen valve, the 69 

Angle, lap 15 

" lead 23 

Angular advance 18 

Angular vibration of the connecting rod 45 

" eccentric rod 49, 85 

Areas of the ports and pipes 42 

Armington & Sims valve, the 73 

Armstrong valve, the 72 

Backward rotation 11,26 

Bilgram diagram, the 28 

" valve gear, the 122 

Buckeye valve gear, the 116 

Cavity, influence of the exhaust , 39 

" width of the exhaust 38 

Centers, locating the engine on the 59 

Clearance, inside 4 

Compression 15,21,23 

Connecting rod, angular vibration of the 45 

" irregularities due to the ........' 5 

' ' of infinite length 47 

Cross-head, the slotted 5 

Cut-off 13,21,23 

' ' and lead equalized 95 

' ' equalized 54 

' ' the slide valve at short 67 

131 



132 INDEX. 



PAGE 

Defects of the primitive engine 13 

Diagram, the Bilgram 28 

Eccentric, position of, for either direction of rotation 27 

rod, angular vibration of the 49> 85 

" " irregularities due to the 5 

the 4 

" shifting 78 

' ' swinging 80 

" throw of the 4 

Engine, the primitive 7 

defectsof 13 

Equalized cut-off 54 

" exhaust. 50, 57 

lead 89 

' ' lead and cut-off 95 

Examples, illustrative 24, 35 

Exhaust cavity, influence of the 39 

width of the 38 

" equalized 50, 57 

" lead 31 

lap 4,25 

1 ' port opening 26, 31 

Gear, the Bilgram valve 122 

" " Buckeye " 116 

" " Gonzenbach valve 102 

" " Meyer " 109 

" " Straight Line " 54,89,120 

Giddings valve, the < 74 

Gonzenbach valve gear, the 102 

Gridiron valve, the 103, 105 

Ide valve, the 74 

Influence of the exhaust cavity 39 

Illustrative examples 24, 35 

Lap .3, 15 

" angle 15 



INDEX. I 33 

Lap, circle page 

" effects of 31 

how measured l8 > 35 

inside or exhaust 4 

' ' negative " ' ' 4. 25 

" outside or steam 4 ' 26 

positive and negative, how shown ' 3 ' * 5 

Lead 31 

' ' and cut-off equalized ' ' " " I3, 2I 

" angle 95 

equal and constant defined 23 

decreasing in early cut-off ' 77 

*' increasing" " « / 82,93,122 

" equalized ^ I 

' ' exhaust " 8 9 

negative 3 1 

Limitations of the plain slide valve 93 

„ v 40 

now overcome 67 

Meyer valve gear, the 

' log 

Negative lead 

93 

Opening, exhaust port 

port 26, 3I 

" definition of'.'.'.'.'.'.'..'.".'/.'.'.*."."."/. l8 ' 3I 

varying width of port " 42 

width of port to steam / 37 

Over-travel of the valve 43 

42, 77 

Pipes and ports, areas of the. 

velocity of steam through the. ' ' ^ 

Piston, speed of, in the two strokes 43 

Port opening 47 

" defined ///.//// l8 ' 3I 

exhaust 4 2 

varying width of .../ 26, 3I 

width of, to steam ' 37 

Ports, length and breadth of. 43 

■'" 44 



134 INDEX. 

PAGE 

Ports, multiple 68, 69, 72 

' ' for the exhaust 70 

Primitive engine , the , 7 

" defects of the 13 

Release » . . * . . .13, 21, 23 

" proper location of the 102 

Reverse rotation 11, 26 

Rice valve, the 72 

Rock shaft 7, 27, 56 

Rod, angular vibration of the connecting 45 

" " " " eccentric 49.85 

' ' connecting, of infinite length 47 

Rotation, reverse 11, 26 

position of eccentric for either direction of 27 

Scotch yoke, the 5 

Setting the slide valve 59 

Shaft, rock 7, 27, 56 

Shifting eccentric, the 78 

Slide valve, laying out the . . 38 

" " limitations of the plain 40 

" how overcome 67 

'-* " setting the 59 

1 ' " the, at short cut-off 67 

" " the plain 3 

Steam, velocity of, through pipes and passages 43 

Straight Line valve, the 69, 120 

" " " gear, the 54,89,120 

Swinging eccentric, the , 80 

Throw of the eccentric 4 

Valve, laying out the slide 38 

" limitations of the plain slide 40 

" " " " " how overcome 67 

" over-travel of the 42, 77 

' ' setting the slide 59 

« ' the Allen 69 



INDEX. 135 

PAGE 

Valve, the Armington & Sims 73 

" " Armstrong 72 

" " Buckeye 116 

" " Giddings , 74 

" " gridiron 103,105 

" " Gonzenbach 102 

" '" Ide... 74 

" " Meyer 109 

" Rice.. 72 

' ' " slide at short cut-off 67 

' ' ' " Straight Line 69, 1 20 

" " plain slide 3 

" ' ' Woodbury 70 

" velocity of the 39 

Valve gear, the Bilgram 122 

" " Buckeye 116 

" " " Gonzenbach 102 

" " " Meyer 109 

" " Straight Line 54, 89, 120 

Velocity of steam through pipes and passages 43 

" of the valve 39 

Vibration of the connecting rod, angular 45 

" " " eccentric " " 49,85 

Width of the exhaust cavity 38 

Woodbury valve, the 70 

Yoke, the Scotch 5 



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